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JEE Three Dimensional Geometry PYQs with Solutions

756 previous year questions from Three Dimensional Geometry (JEE Main & Advanced Mathematics) with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

756 questionsMathematics2006–2026Answers + solutions

About Three Dimensional Geometry PYQs

Three Dimensional Geometry has 756 previous year questions in the Quantrex Academy JEE Main & Advanced Mathematics bank. The 220 questions in this list come from JEE Main (181) and JEE Advanced (39), spanning 2006 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

Questions by year (this list)

  • 2026: 34
  • 2025: 37
  • 2024: 47
  • 2023: 71
  • 2022: 2
  • 2020: 2
  • 2019: 3
  • 2018: 2
  • 2017: 1
  • 2016: 2
  • 2015: 2
  • 2014: 1

Three Dimensional Geometry questions with solutions

1

Let P be the plane such that it contains the straight line (x-1)/(2) = (y-3)/(3) = (z+2)/(1) and is perpendicular to the plane x + 2y + 3z = 4 . Let P_1 be the plane which passes

JEE Advanced 2026 Solution View → 2

Let L be the straight line joining the points P(1, 2, -1) and Q(2, 3, 1) . Let S be the foot of the perpendicular drawn from the point R(4, -1, 5) to the line L . Another line

JEE Advanced 2026 Solution View → 3

Let the foot of perpendicular from the point (λ, 2, 3) on the line (x-4)/(1) = (y-9)/(2) = (z-5)/(1) be the point (1, μ, 2) . Then the distance between the lines (x-1)/(2) =

JEE Main 2026 Solution View → 4

Let a line L_1 pass through the origin and be perpendicular to the lines L_2: r = (3+t) i + (2t-1) j + (2t+4) k and L_3: r = (3+2s) i + (3+2s) j + (2+s) k , t, s ∈ ℝ . If (a, b

JEE Main 2026 Solution View → 5

The shortest distance between the lines (x-4)/(1) = (y-3)/(2) = (z-2)/(-3) and (x+2)/(2) = (y-6)/(4) = (z-5)/(-5) is :

JEE Main 2026 Solution View → 6

Let the image of the point P(0, -5, 0) in the line (x-1)/(2) = (y)/(1) = (z+1)/(-2) be the point R and the image of the point Q(0, (-1)/(2), 0) in the line (x-1)/(-1) = (y+9)/(4)

JEE Main 2026 Solution View → 7

Let the image of the point P(1, 6, a) in the line L: (x)/(1) = (y-1)/(2) = (z-a+1)/(b) , b > 0 , be ((a)/(3), 0, a+c) . If S(α, β, γ) , α > 0 , is the point on L such that the

JEE Main 2026 Solution View → 8

Let a line L be perpendicular to both the lines L_1: (x+1)/(3) = (y+3)/(5) = (z+5)/(7) and L_2: (x-2)/(1) = (y-4)/(4) = (z-6)/(7) . If θ is the acute angle between the lines L and

JEE Main 2026 Solution View → 9

Let a triangle PQR be such that P and Q lie on the line (x+3)/(8) = (y-4)/(2) = (z+1)/(2) and are at a distance of 6 units from R(1, 2, 3) . If (α, β, γ) is the centroid of PQR

JEE Main 2026 Solution View → 10

If the distance of the point (a, 2, 5) from the image of the point (1, 2, 7) in the line (x)/(1) = (y-1)/(1) = (z-2)/(2) is 4 , then the sum of all possible values of a is equal

JEE Main 2026 Solution View → 11

The square of the distance of the point P(5, 6, 7) from the line (x-2)/(2) = (y-5)/(3) = (z-2)/(4) is equal to:

JEE Main 2026 Solution View → 12

The square of the distance of the point of intersection of the lines r = ( i + j - k ) + λ(a i - j ) , a ≠ 0 and r = (4 i - k ) + μ(2 i + a k ) from the origin is:

JEE Main 2026 Solution View → 13

The shortest distance between the lines r =((1)/(3) i +2 j +(8)/(3) k )+λ(2 i -5 j +6 k ) and r =(-(2)/(3) i -(1)/(3) k )+μ( j - k ) , λ,μ ∈ ℝ , is:

JEE Main 2026 Solution View → 14

If (2α+1, α^2-3α, (α-1)/(2)) is the image of (α, 2α, 1) in the line (x-2)/(3)=(y-1)/(2)=(z)/(1) , then the possible value(s) of α is (are)

JEE Main 2026 Solution View → 15

A line with direction ratios 1, -1, 2 intersects the lines (x)/(2) = (y)/(3) = (z+1)/(3) and (x+1)/(-1) = (y-2)/(1) = (z)/(4) at the points P and Q , respectively. If the length

JEE Main 2026 Solution View → 16

The square of the distance of the point (-2, -8, 6) from the line (x-1)/(1) = (y-1)/(2) = (z)/(-1) along the line (x+5)/(1) = (y+5)/(-1) = (z)/(2) is equal to:

JEE Main 2026 Solution View → 17

Let the point A be the foot of perpendicular drawn from the point P(a, b, 0) on the line (x-1)/(2) = (y-2)/(1) = (z-α)/(3) . If the midpoint of the line segment PA is (0, (3)/(4)

JEE Main 2026 Solution View → 18

If the point of intersection of the lines (x+1)/(3) = (y+a)/(5) = (z+b+1)/(7) and (x-2)/(1) = (y-b)/(4) = (z-2a)/(7) lies on xy -plane, then the value of a + b is :

JEE Main 2026 Solution View → 19

Let a line L passing through the point (1, 1, 1) be perpendicular to both the vectors 2 i + 2 j + k and i + 2 j + 2 k . If P(a, b, c) is the foot of perpendicular from the origin

JEE Main 2026 Solution View → 20

Let Q(a, b, c) be the image of the point P(3,2,1) in the line (x-1)/(1)=(y)/(2)=(z-1)/(1) . Then the distance of Q from the line (x-9)/(3)=(y-9)/(2)=(z-5)/(-2) is

JEE Main 2026 Solution View → 21

If the distance of the point P(43, α, β), β<0 , from the line r =4 i - k +μ(2 i +3 k ), μ ∈ R along a line with direction ratios 3,-1,0 is 13 10 , then α^ 2 +β^ 2 is equal to

JEE Main 2026 Solution View → 22

If the distances of the point (1,2, a) from the line (x-1)/(1)=(y)/(2)=(z-1)/(1) along the lines L_ 1 : (x-1)/(3)=(y-2)/(4)=(z-a)/(b) and L_ 2 : (x-1)/(1)=(y-2)/(4)=(z-a)/(c) are

JEE Main 2026 Solution View → 23

The sum of all values of α , for which the shortest distance between the lines (x+1)/(α)=(y-2)/(-1)=(z-4)/(-α) and (x)/(α)=(y-1)/(2)=(z-1)/(2 α) is 2 , is

JEE Main 2026 Solution View → 24

Let the lines L_ 1 : r = i +2 j +3 k +λ(2 i +3 j +4 k ), λ ∈ ℝ and L_ 2 : r =(4 i + j )+μ(5 i +2 j + k ), μ ∈ ℝ , intersect at the point R. Let P and Q be the points lying on

JEE Main 2026 Solution View → 25

Let a line L passing through the point P(1,1,1) be perpendicular to the lines (x-4)/(4)=(y-1)/(1)=(z-1)/(1) and (x-17)/(1)=(y-71)/(1)=(z)/(0) . Let the line L intersect the y z

JEE Main 2026 Solution View → 26

If the image of the point P(a, 2, a) in the line (x)/(2)=(y+a)/(1)=(z)/(1) is Q and the image of Q in the line (x-2 b)/(2)=(y-a)/(1)=(z+2 b)/(-5) is P, then a+b is equal to

JEE Main 2026 Solution View → 27

Let the direction cosines of two lines satisfy the equations : 4 l+m-n=0 and 2 m n+10 n l+3 l m=0 . Then the cosine of the acute angle between these lines is :

JEE Main 2026 Solution View → 28

The vertices B and C of a triangle ABC lie on the line (x)/(1)=(1-y)/(-2)= z-2 3 . The coordinates of A and B are (1,6,3) and (4,9, α) respectively and C is at a distance of 10

JEE Main 2026 Solution View → 29

Let L be the line (x+1)/(2)=(y+1)/(3)=(z+3)/(6) and let S be the set of all points (a, b, c) on L, whose distance from the line (x+1)/(2)=(y+1)/(3)=(z-9)/(0) along the line L is

JEE Main 2026 Solution View → 30

If the image of the point P(1,2, a) in the line (x-6)/(3)=(y-7)/(2)= 7-z 2 is Q(5, b, c) , then a^ 2 +b^ 2 +c^ 2 is equal to

JEE Main 2026 Solution View → 31

Let P(α, β, γ) be the point on the line (x-1)/(2)=(y+1)/(-3)=z at a distance 4 14 from the point (1,-1,0) and nearer to the origin. Then the shortest distance, between the lines

JEE Main 2026 Solution View → 32

Let the line L pass through the point (-3,5,2) and make equal angles with the positive coordinate axes. If the distance of L from the point (-2, r, 1) is (14)/(3) , then the sum

JEE Main 2026 Solution View → 33

Let the line L_ 1 be parallel to the vector -3 i +2 j +4 k and pass through the point (2,6,7), and the line L_ 2 be parallel to the vector 2 i + j +3 k and pass through the point

JEE Main 2026 Solution View → 34

Let (α, β, γ) be the co-ordinates of the foot of the perpendicular drawn from the point (5,4,2) on the line r =(- i +3 j + k )+λ(2 i +3 j - k ) . Then the length of the projection

JEE Main 2026 Solution View → 35

Let L_1 be the line of intersection of the planes given by the equation- 2 x+3 y+z=4 and x+2 y+z=5 . Let L_2 be the line passing through the point P(2,-1,3) and parallel to L_1 .

JEE Advanced 2025 Solution View → 36

Let the values of λ for which the shortest distance between the lines (x-1)/(2)=(y-2)/(3)=(z-3)/(4) and (x-λ)/(3)=(y-4)/(4)=(z-5)/(5) is 1 6 be λ_1 and λ_2 . Then the radius of

JEE Main 2025 Solution View → 37

Let the area of the triangle formed by the lines x+2=y-1=z, (x-3)/(5)=(y)/(-1)=(z-1)/(1) and (x)/(-3)=(y-3)/(3)=(z-2)/(1) be A . Then A^2 is equal to ________

JEE Main 2025 Solution View → 38

Consider the lines L_1: x-1=y-2=z and L_2: x-2=y=z-1 . Let the feet of the perpendiculars from the point P(5,1,-3) on the lines L_1 and L_2 be Q and R respectively. If the area of

JEE Main 2025 Solution View → 39

If the equation of the line passing through the point (0,-(1)/(2), 0) and perpendicular to the lines r =λ( i +a j +b k ) and r =( i - j -6 k )+μ(-b i +a j +5 k ) is x-1 -2 = y+4

JEE Main 2025 Solution View → 40

If the shortest distance between the lines (x-1)/(2)=(y-2)/(3)=(z-3)/(4) and (x)/(1)=(y)/(α)=(z-5)/(1) is 5 6 , then the sum of all possible values of α is

JEE Main 2025 Solution View → 41

Let the line L pass through (1,1,1) and intersect the lines (x-1)/(2)=(y+1)/(3)=(z-1)/(4) and (x-3)/(1)=(y-4)/(2)=(z)/(1) . Then, which of the following points lies on the line L ?

JEE Main 2025 Solution View → 42

Let the values of p , for which the shortest distance between the lines (x+1)/(3)=(y)/(4)=(z)/(5) and r =(p i +2 j + k )+λ(2 i +3 j +4 k ) is 1 6 , be a, b , (a b) . Then the

JEE Main 2025 Solution View → 43

Let A be the point of intersection of the lines L_1: (x-7)/(1)=(y-5)/(0)=(z-3)/(-1) and L_2: (x-1)/(3)=(y+3)/(4)=(z+7)/(5) . Let B and C be the point on the lines L_1 and L_2

JEE Main 2025 Solution View → 44

Let the shortest distance between the lines (x-3)/(3)=(y-α)/(-1)=(z-3)/(1) and (x+3)/(-3)=(y+7)/(2)=(z-β)/(4) be 3 30 . Then the positive value of 5 α+β is

JEE Main 2025 Solution View → 45

Let A and B be two distinct points on the line L: x-6 3 = y-7 2 = z-7 -2 . Both A and B are at a distance 2 17 from the foot of perpendicular drawn from the point (1,2,3) on the

JEE Main 2025 Solution View → 46

Each of the angles β and γ that a given line makes with the positive y - and z -axes, respectively, is half of the angle that this line makes with the positive x -axes. Then the

JEE Main 2025 Solution View → 47

The distance of the point (7,10,11) from the line (x-4)/(1)=(y-4)/(0)=(z-2)/(3) along the line (x-9)/(2)=(y-13)/(3)=(z-17)/(6) is

JEE Main 2025 Solution View → 48

Let a line passing through the point (4,1,0) intersect the line L_1 ; (x-1)/(2)=(y-2)/(3)=(z-3)/(4) at the point A (α, β, γ) and the line L_2: x-6=y=-z+4 at the point B(a, b, c) .

JEE Main 2025 Solution View → 49

Line L_1 passes through the point (1,2,3) and is parallel to Z -axis. Line L_2 passes through the point (λ, 5,6) and is parallel to y -axis. Let for λ=λ_1, λ_2, λ_2 λ_1 , the

JEE Main 2025 Solution View → 50

The line L_1 is parallel to the vector a =-3 i +2 j +4 k and passes through the point (7,6,2) and the line L_2 is parallel to the vector b =2 i + j +3 k and passes through the

JEE Main 2025 Solution View → 51

If the image of the point P(1,0,3) in the line joining the points A(4,7,1) and B(3,5,3) is Q(α, β, γ) , then α+β+γ is equal to

JEE Main 2025 Solution View → 52

Let the vertices Q and R of the triangle P Q R lie on the line (x+3)/(5)=(y-1)/(2)=(z+4)/(3), Q R=5 and the coordinates of the point P be (0,2,3) . If the area of the triangle P Q

JEE Main 2025 Solution View → 53

Let P be the foot of the perpendicular from the point (1,2,2) on the line L: (x-1)/(1)=(y+1)/(-1)=(z-2)/(2) . Let the line r =(- i + j -2 k )+λ( i - j + k ), λ ∈ R , intersect the

JEE Main 2025 Solution View → 54

Let a straight line L pass through the point P(2,-1,3) and be perpendicular to the lines (x-1)/(2)=(y+1)/(1)=(z-3)/(-2) and (x-3)/(1)=(y-2)/(3)=(z+2)/(4) . If the line L

JEE Main 2025 Solution View → 55

Let \( a = i + 2 j + k \) and \( b = 2 i +7 j +3 k . \) Let \( L _ 1 : r =(- i +2 j + k )+λ a , λ ∈ R\) and \( L _ 2 : r =( j + k )+μ b , μ ∈ R \) be two lines. If the line \( L _

JEE Main 2025 Solution View → 56

Let \(L _ 1 : (x-1)/(1)=(y-2)/(-1)=(z-1)/(2)\) and \( L _ 2 : (x+1)/(-1)=(y-2)/(2)=(z)/(1) \) be two lines. Let \(L_3\) be a line passing through the point \((α, β, γ) \) and be

JEE Main 2025 Solution View → 57

The square of the distance of the point ((15)/(7), (32)/(7), 7) from the line (x+1)/(3)=(y+3)/(5)=(z+5)/(7) in the direction of the vector i +4 j +7 k is :

JEE Main 2025 Solution View → 58

If the image of the point (4,4,3) in the line (x-1)/(2)=(y-2)/(1)=(z-1)/(3) is (α, β, γ) , then α+β+γ is equal to

JEE Main 2025 Solution View → 59

Let A(x, y, z) be a point in x y -plane, which is equidistant from three points (0,3,2),(2,0,3) and ( 0,0,1 ). Let B=(1,4,-1) and C=(2,0,-2) . Then among the statements (S1) : ABC

JEE Main 2025 Solution View → 60

Let P be the image of the point Q(7,-2,5) in the line L: (x-1)/(2)=(y+1)/(3)=(z)/(4) and R(5, p, q) be a point on L . Then the square of the area of P Q R is ________.

JEE Main 2025 Solution View → 61

Let in a A B C , the length of the side A C be 6 , the vertex B be (1,2,3) and the vertices A, C lie on the line (x-6)/(3)=(y-7)/(2)=(z-7)/(-2) . Then the area (in sq. units) of

JEE Main 2025 Solution View → 62

Let the line passing through the points (-1,2,1) and parallel to the line (x-1)/(2)=(y+1)/(3)=(z)/(4) intersect the line (x+2)/(3)=(y-3)/(2)=(z-4)/(1) at the point P . Then the

JEE Main 2025 Solution View → 63

The distance of the line (x-2)/(2)=(y-6)/(3)=(z-3)/(4) from the point (1,4,0) along the line (x)/(1)=(y-2)/(2)=(z+3)/(3) is :

JEE Main 2025 Solution View → 64

If the square of the shortest distance between the lines (x-2)/(1)=(y-1)/(2)=(z+3)/(-3) and (x+1)/(2)=(y+3)/(4)=(z+5)/(-5) is m n , where m, n are coprime numbers, then m+n is

JEE Main 2025 Solution View → 65

Let the point A divide the line segment joining the points P(-1,-1,2) and Q(5,5,10) internally in the ratio r: 1(r 0) . If O is the origin and ( OQ · OA )-(1)/(5)| OP × OA |^2=10

JEE Main 2025 Solution View → 66

Let P be the foot of the perpendicular from the point Q(10,-3,-1) on the line (x-3)/(7)=(y-2)/(-1)=(z+1)/(-2) . Then the area of the right angled triangle P Q R , where R is the

JEE Main 2025 Solution View → 67

Let a line pass through two distinct points P(-2,-1,3) and Q , and be parallel to the vector 3 i +2 j +2 k . If the distance of the point Q from the point R(1,3,3) is 5 , then the

JEE Main 2025 Solution View → 68

The perpendicular distance, of the line (x-1)/(2)=(y+2)/(-1)=(z+3)/(2) from the point P(2,-10,1) , is :

JEE Main 2025 Solution View → 69

Let the distance between two parallel lines be 5 units and a point P lie between the lines at a unit distance from one of them. An equilateral triangle P Q R is formed such that Q

JEE Main 2025 Solution View → 70

Let L_1: (x-1)/(2)=(y-2)/(3)=(z-3)/(4) and L_2: (x-2)/(3)=(y-4)/(4)=(z-5)/(5) be two lines. Then which of the following points lies on the line of the shortest distance between

JEE Main 2025 Solution View → 71

Let L_1: (x-1)/(3)=(y-1)/(-1)=(z+1)/(0) and L_2: (x-2)/(2)=(y)/(0)=(z+4)/(α), α ∈ R , be two lines, which intersect at the point B . If P is the foot of perpendicular from the

JEE Main 2025 Solution View → 72

A straight line drawn from the point P(1,3,2) , parallel to the line (x-2)/(1)=(y-4)/(2)=(z-6)/(1) , intersects the plane L_1: x-y+3 z=6 at the point Q . Another straight line

JEE Advanced 2024 Solution View → 73

Let ℝ^3 denote the three-dimensional space. Take two points P=(1,2,3) and Q=(4,2,7) . Let dist(X, Y) denote the distance between two points X and Y in ℝ^3 . Let gathered S=\ X ∈

JEE Advanced 2024 Solution View → 74

Let γ ∈ ℝ be such that the lines L_1: (x+11)/(1)= y+21 2 = z+29 3 and L_2: (x+16)/(3)=(y+11)/(2)=(z+4)/(γ) intersect. Let R_1 be the point of intersection of L_1 and L_2 . Let

JEE Advanced 2024 Solution View → 75

Consider the line L passing through the points (1,2,3) and (2,3,5) . The distance of the point ((11)/(3), (11)/(3), (19)/(3)) from the line L along the line (3 x-11)/(2)=(3

JEE Main 2024 Solution View → 76

The square of the distance of the image of the point (6,1,5) in the line (x-1)/(3)=(y)/(2)=(z-2)/(4) , from the origin is _________

JEE Main 2024 Solution View → 77

Let the line L intersect the lines x-2=-y=z-1,2(x+1)=2(y-1)=z+1 and be parallel to the line (x-2)/(3)=(y-1)/(1)=(z-2)/(2) . Then which of the following points lies on L?

JEE Main 2024 Solution View → 78

The shortest distance between the lines (x-3)/(4)=(y+7)/(-11)=(z-1)/(5) and (x-5)/(3)=(y-9)/(-6)=(z+2)/(1) is:

JEE Main 2024 Solution View → 79

If the shortest distance between the lines (x-λ)/(2)=(y-4)/(3)=(z-3)/(4) and (x-2)/(4)=(y-4)/(6)=(z-7)/(8) is 13 29 , then a value of λ is :

JEE Main 2024 Solution View → 80

Let P(α, β, γ) be the image of the point Q(1,6,4) in the line (x)/(1)=(y-1)/(2)=(z-2)/(3) . Then 2 α+β+γ is equal to_______

JEE Main 2024 Solution View → 81

If the shortest distance between the lines array ll L_1: r =(2+λ) i +(1-3 λ) j +(3+4 λ) k , & λ ∈ ℝ L_2: r =2(1+μ) i +3(1+μ) j +(5+μ) k , μ ∈ ℝ array is m n , where gcd(m, n)=1

JEE Main 2024 Solution View → 82

Let P(x, y, z) be a point in the first octant, whose projection in the x y -plane is the point Q . Let O P=γ ; the angle between O Q and the positive x -axis be θ ; and the angle

JEE Main 2024 Solution View → 83

Let P(α, β, γ) be the image of the point Q(3,-3,1) in the line (x-0)/(1)=(y-3)/(1)=(z-1)/(-1) and R be the point (2,5,-1) . If the area of the triangle P Q R is λ and λ^2=14 K

JEE Main 2024 Solution View → 84

If the shortest distance between the lines (x-λ)/(3)=(y-2)/(-1)=(z-1)/(1) and (x+2)/(-3)=(y+5)/(2)=(z-4)/(4) is 44 30 , then the largest possible value of |λ| is equal to _________

JEE Main 2024 Solution View → 85

The shortest distance between the lines (x-3)/(2)=(y+15)/(-7)=(z-9)/(5) and (x+1)/(2)=(y-1)/(1)=(z-9)/(-3) is

JEE Main 2024 Solution View → 86

Let P be the point (10,-2,-1) and Q be the foot of the perpendicular drawn from the point R(1,7,6) on the line passing through the points (2,-5,11) and (-6,7,-5) . Then the length

JEE Main 2024 Solution View → 87

Let (α, β, γ) be the image of the point (8,5,7) in the line (x-1)/(2)=(y+1)/(3)=(z-2)/(5) . Then α+β+γ is equal to :

JEE Main 2024 Solution View → 88

Let the point (-1, α, β) lie on the line of the shortest distance between the lines (x+2)/(-3)=(y-2)/(4)=(z-5)/(2) and (x+2)/(-1)=(y+6)/(2)=(z-1)/(0) . Then (α-β)^2 is equal

JEE Main 2024 Solution View → 89

If the line (2-x)/(3)=(3 y-2)/(4 λ+1)=4-z makes a right angle with the line (x+3)/(3 μ)=(1-2 y)/(6)=(5-z)/(7) , then 4 λ+9 μ is equal to :

JEE Main 2024 Solution View → 90

Let d be the distance of the point of intersection of the lines (x+6)/(3)=(y)/(2)=(z+1)/(1) and (x-7)/(4)=(y-9)/(3)=(z-4)/(2) from the point (7,8,9) . Then d^2+6 is equal to :

JEE Main 2024 Solution View → 91

Let P be the point of intersection of the lines (x-2)/(1)=(y-4)/(5)=(z-2)/(1) and (x-3)/(2)=(y-2)/(3)=(z-3)/(2) . Then, the shortest distance of P from the line 4 x=2 y=z is

JEE Main 2024 Solution View → 92

Consider a line L passing through the points P(1,2,1) and Q(2,1,-1) . If the mirror image of the point A(2,2,2) in the line L is (α, β, γ) , then α+β+6 γ is equal to _______

JEE Main 2024 Solution View → 93

Let the point, on the line passing through the points P(1,-2,3) and Q(5,-4,7) , farther from the origin and at distance of 9 units from the point P , be (α, β, γ) . Then

JEE Main 2024 Solution View → 94

If the shortest distance between the lines (x+2)/(2)=(y+3)/(3)=(z-5)/(4) and (x-3)/(1)=(y-2)/(-3)=(z+4)/(2) is 38 3 5 k , and ∫_0^ k [x^2] d x=α- α , where [x] denotes the

JEE Main 2024 Solution View → 95

If the mirror image of the point P ( 3, 4, 9 ) in the line (x - 1)/(3) = (y + 1)/(2) = (z - 2)/(1) is (α, β, γ), then 14 (α + β + γ) is:

JEE Main 2024 Solution View → 96

Let PandQ be the points on the line (x + 3)/(8) = (y - 4)/(2) = (z + 1)/(2) which are at a distance of 6 units from the point R ( 1, 2, 3 ) . If the centroid of the triangle PQR

JEE Main 2024 Solution View → 97

If the shortest distance between the lines (x - λ)/(- 2) = (y - 2)/(1) = (z - 1)/(1) and x - 3 1 = (y - 1)/(- 2) = (z - 2)/(1) is 1 , then the sum of all possible values of λ is

JEE Main 2024 Solution View → 98

Let the line of the shortest distance between the lines L _ 1 : → r = ( ^ i + 2 ^ j + 3 ^ k ) + λ ( ^ i - ^ j + ^ k ) and L _ 2 : → r =(4 ^ i + 5 ^ j + 6 ^ k ) + μ ( ^ i + ^ j - ^

JEE Main 2024 Solution View → 99

Let (α, β, γ) be mirror image of the point (2, 3, 5) in the line (x - 1)/(2) = (y - 2)/(3) = (z - 3)/(4) . Then 2α + 3β + 4γ is equal to

JEE Main 2024 Solution View → 100

The shortest distance between lines L _ 1 and L _ 2 , where L _ 1 : (x - 1)/(2) = (y + 1)/(- 3) = (z + 4)/(2) and L _ 2 is the line passing through the points A(- 4, 4, 3), B(- 1

JEE Main 2024 Solution View → 101

A line passes through A(4, - 6, - 2) and B(16, - 2, 4) . The point P(a, b, c) where a, b, c are non-negative integers, on the line AB lies at a distance of 21 units, from the

JEE Main 2024 Solution View → 102

The distance of the point Q ( 0, 2, – 2 ) form the line passing through the point P ( 5, – 4, 3 ) and perpendicular to the lines → r = (- 3 ^ i + 2 ^ k ) + λ(2 ^ i + 3 ^ j + 5 ^ k

JEE Main 2024 Solution View → 103

Let Q and R be the feet of perpendiculars from the point P(a, a, a) on the lines x = y, z = 1 and x = - y, z = - 1 respectively. If ∠ QPR is a right angle, then 12 a ^ 2 is equal

JEE Main 2024 Solution View → 104

Let L _ 1 : → r = ( ^ i - ^ j + 2 ^ k ) + λ( ^ i - ^ j + 2 ^ k ), λ ∈ R , L _ 2 : → r = ( ^ j - ^ k ) + μ(3 ^ i + ^ j + p ^ k ), μ ∈ R and L _ 3 : → r = δ ( l ^ i + m ^ j + n ^ k

JEE Main 2024 Solution View → 105

Let a line passing through the point ( - 1, 2, 3 ) intersect the lines L _ 1 : (x - 1)/(3) = (y - 2)/(2) = (z + 1)/(- 2) at M ( α, β, γ ) and L _ 2 : (x + 2)/(- 3) = (y - 2)/(- 2)

JEE Main 2024 Solution View → 106

Let ( α, β, γ ) be the foot of perpendicular from the point ( 1, 2, 3 ) on the line (x + 3)/(5) = (y - 1)/(2) = (z + 4)/(3) . then 19 ( α + β + γ ) is equal to :

JEE Main 2024 Solution View → 107

If d _ 1 is the shortest distance between the lines x + 1 = 2y = - 12z, x = y + 2 = 6z - 6 and d _ 2 is the shortest distance between the lines (x - 1)/(2) = (y + 8)/(- 7) = (z

JEE Main 2024 Solution View → 108

Let P ( 3, 2, 3 ) , Q ( 4, 6, 2 ) and R ( 7, 3, 2 ) be the vertices of ∆ PQR . Then, the angle ∠ QPR is

JEE Main 2024 Solution View → 109

Let O be the origin, and M and N be the points on the lines (x - 5)/(4) = (y - 4)/(1) = (z - 5)/(3) and (x + 8)/(12) = (y + 2)/(5) = (z + 11)/(9) respectively such that MN is the

JEE Main 2024 Solution View → 110

Let O be the origin and the position vector of A and B be 2 ^ i + 2 ^ j + ^ k and 2 ^ i + 4 ^ j + 4 ^ k respectively. If the internal bisector of ∠ AOB meets the line AB at C

JEE Main 2024 Solution View → 111

Let PQR be a triangle with R ( - 1, 4, 2 ) . Suppose M ( 2, 1, 2 ) is the mid point of PQ . The distance of the centroid of ∆ PQR from the point of intersection of the line (x

JEE Main 2024 Solution View → 112

A line with direction ratio 2, 1, 2 meets the lines x = y + 2 = z and x + 2 = 2y = 2z respectively at the point P and Q . if the length of the perpendicular from the point ( 1, 2

JEE Main 2024 Solution View → 113

The position vectors of the vertices A, B and C of a triangle are 2 ^ i - 3 ^ j + 3 ^ k , 2 ^ i + 2 ^ j + 3 ^ k and - ^ i + ^ j + 3 ^ k respectively. Let l denotes the length of

JEE Main 2024 Solution View → 114

Let the position vectors of the vertices A, B and C of a triangle be 2 ^ i + 2 ^ j + ^ k , ^ i + 2 ^ j + 2 ^ k and 2 ^ i + ^ j + 2 ^ k respectively. Let l _ 1 , l _ 2 and l _ 3 be

JEE Main 2024 Solution View → 115

The lines (x - 2)/(2) = (y)/(- 2) = (z - 7)/(16) and (x + 3)/(4) = (y + 2)/(3) = (z + 2)/(1) intersect at the point P . If the distance of P from the line (x + 1)/(2) = (y

JEE Main 2024 Solution View → 116

Let the image of the point ( 1, 0, 7 ) in the line (x)/(1) = (y - 1)/(2) = (z - 2)/(3) be the point ( α, β, γ ) . Then which one of the following points lies on the line passing

JEE Main 2024 Solution View → 117

The distance, of the point ( 7, - 2, 11 ) from the line (x - 6)/(1) = (y - 4)/(0) = (z - 8)/(3) along the line (x - 5)/(2) = (y - 1)/(- 3) = (z - 5)/(6) , is :

JEE Main 2024 Solution View → 118

If the shortest distance between the lines (x - 4)/(1) = (y + 1)/(2) = (z)/(- 3) and (x - λ)/(2) = (y + 1)/(4) = (z - 2)/(- 5) is 6 5 , then the sum of all possible values of λ is

JEE Main 2024 Solution View → 119

Let Q be the cube with the set of vertices \ ( x _ 1 , x _ 2 , x _ 3 ) ∈ ℝ ^ 3 : x _ 1 , x _ 2 , x _ 3 ∈ \ 0, 1\ \ . Let F be the set of all twelve lines containing the diagonals

JEE Advanced 2023 Solution View → 120

Let ℓ _ 1 and ℓ _ 2 be the lines → r 1 = λ( ^ i + ^ j + ^ k ) and → r 2 = ( ^ j - ^ k ) + μ( ^ i + ^ k ) , respectively, Let X be the set of all the planes H that contain the line

JEE Advanced 2023 Solution View → 121

Let the foot of perpendicular of the point P(3, – 2, – 9) on the plane passing through the points (– 1, – 2, – 3), (9, 3, 4), (9, – 2, 1) be Q (α, β, γ) . Then the distance Q from

JEE Main 2023 Solution View → 122

Let S be the set of all values of λ , for which the shortest distance between the lines (x - λ)/(0) = (y - 3)/(4) = (z + 6)/(1) and (x + λ)/(3) = (y)/(- 4) = (z - 6)/(0) is 13 .

JEE Main 2023 Solution View → 123

If the line x = y = z intersects the line xsinA + ysinB + zsinC - 18 = 0 = xsin2A + ysin2B + zsin2C - 9 , where A, B, C are the angles of a triangle ABC , then

JEE Main 2023 Solution View → 124

Let the plane P contain the line 2x + y - z - 3 = 0 = 5x - 3y + 4z + 9 and be parallel to the line (x + 2)/(2) = (3 - y)/(- 4) = (z - 7)/(5) . Then the distance of the point A(8

JEE Main 2023 Solution View → 125

The plane, passing through the points ( 0, – 1, 2 ) and ( – 1, 2, 1 ) and parallel to the line passing through ( 5, 1, – 7 ) and ( 1, – 1, – 1 ) , also passes through the point

JEE Main 2023 Solution View → 126

The line, that is coplanar to the line (x + 3)/(- 3) = (y - 1)/(1) = (z - 5)/(5) , is

JEE Main 2023 Solution View → 127

Let N be the foot of perpendicular from the point P ( 1, - 2, 3 ) on the line passing through the points ( 4, 5, 8 ) and ( 1, - 7, 5 ) . Then the distance of N from the plane 2x

JEE Main 2023 Solution View → 128

Let the equation of plane passing through the line of intersection of the planes x + 2y + az = 2 and x - y + z = 3 be 5x - 11y + bz = 6a - 1 . For c ∈ ℤ, if the distance of this

JEE Main 2023 Solution View → 129

The distance of the point (- 1, 2, 3) from the plane → r · ( ^ i - 2 ^ j + 3 ^ k ) = 10 parallel to the line of the shortest distance between the lines → r = ( ^ i - ^ j ) + λ ( 2

JEE Main 2023 Solution View → 130

Let the image of the point ((5)/(3), (5)/(3), (8)/(3)) in the plane x - 2y + z – 2 = 0 be P . If the distance of the point Q ( 6, - 2, α ) , α > 0, from P is 13, then α is equal

JEE Main 2023 Solution View → 131

Let the lines L _ 1 : (x + 5)/(3) = (y + 4)/(1) = (z - α)/(- 2) and L _ 2 : 3x + 2y + z - 2 = 0 = x - 3y + 2z - 13 be coplanar. If the point P(a, b, c) on L _ 1 is nearest to the

JEE Main 2023 Solution View → 132

Let the plane P: 4x - y + z = 10 be rotated by an angle (π)/(2) about its line of intersection with the plane x + y - z = 4 . If α is the distance of the point ( 2, 3, - 4 ) from

JEE Main 2023 Solution View → 133

Let P be the plane passing through the points (5, 3, 0), (13, 3, - 2) and (1, 6, 2). For α ∈ ℕ , if the distance of the pointsA (3, 4, α) and B (2, α, a) from the plane P are 2

JEE Main 2023 Solution View → 134

Let the line passing through the points P(2, - 1, 2) and Q(5, 3, 4) meet the plane x - y + z = 4 at the point R . Then the distance of the point R from the plane x + 2y + 3z + 2 =

JEE Main 2023 Solution View → 135

Let the line L: x = (1 - y)/(- 2) = (z - 3)/(λ), λ ∈ ℝ meet the plane P: x + 2y + 3z = 4 at the point ( α, β, γ ) . If the angle between the line L and the plane P is ^ - 1 (

JEE Main 2023 Solution View → 136

Let ( α, β, γ ) be the image of point P ( 2, 3, 5 ) in the plane 2x + y - 3z = 6 . Then α + β + γ is equal to

JEE Main 2023 Solution View → 137

If the equation of the plane that contains the point ( - 2, 3, 5 ) and is perpendicular to each of the planes 2x + 4y + 5z = 8 and 3x - 2y + 3z = 5 is + + + 97 = 0 then α + β + γ =

JEE Main 2023 Solution View → 138

Let a line L pass through the origin and be perpendicular to the lines L _ 1 : → r = ( ^ i - 11 ^ j - 7 ^ k ) + λ( ^ i + 2 ^ j + 3 ^ k ), λ ∈ ℝ and L _ 2 : → r = (- ^ i + ^ k ) +

JEE Main 2023 Solution View → 139

Let the image of the point P ( 1, 2, 6 ) in the plane passing through the points A ( 1, 2, 0 ) and B ( 1, 4, 1 ) C ( 0, 5, 1 ) be Q ( α, β, γ ) . Then ( α ^ 2 + β ^ 2 + γ ^ 2 )

JEE Main 2023 Solution View → 140

Let the line (x)/(1) = (6 - y)/(2) = (z + 8)/(5) intersect the lines (x - 5)/(4) = (y - 7)/(3) = (z + 2)/(1) and (x + 3)/(6) = (3 - y)/(3) = (z - 6)/(1) at the points A and B

JEE Main 2023 Solution View → 141

Let the foot of perpendicular from the point A(4, 3, 1) on the plane P: x - y + 2z + 3 = 0 be N . If B ( 5, α, β ) , α, β ∈ ℤ is a point on plane P such that the area of the

JEE Main 2023 Solution View → 142

Let two vertices of a triangle ABC be (2, 4, 6) and (0, - 2, - 5) , and its centroid be (2, 1, - 1) . If the image of the third vertex in the plane x + 2y + 4z = 11 is (α, β, γ)

JEE Main 2023 Solution View → 143

The shortest distance between the lines (x + 2)/(1) = (y)/(- 2) = (z - 5)/(2) and (x - 4)/(1) = (y - 1)/(2) = (z + 3)/(0) is

JEE Main 2023 Solution View → 144

Let P be the point of intersection of the line (x + 3)/(3) = (y + 2)/(1) = (1 - z)/(2) and the plane x + y + z = 2 . If the distance of the point P from the plane 3x - 4y + 12z =

JEE Main 2023 Solution View → 145

For a, b ∈ Z and | a - b | ≤ 10 , let the angle between the plane P: ax + y - z = b and the line L: x - 1 = a - y = z + 1 be ^ - 1 ((1)/(3)) If the distance of the point ( 6, - 6

JEE Main 2023 Solution View → 146

Let P be the plane passing through the line (x - 1)/(1) = (y - 2)/(- 3) = (z + 5)/(7) and the point ( 2, 4, - 3 ) . If the image of the point ( - 1, 3, 4 ) in the plane P is ( α

JEE Main 2023 Solution View → 147

Let P _ 1 be the plane 3x - y - 7z = 11 and P _ 2 be the plane passing through the points ( 2, - 1, 0 ) , ( 2, 0, - 1 ) , and ( 5, 1, 1 ) . If the foot of the perpendicular drawn

JEE Main 2023 Solution View → 148

The shortest distance between the lines (x - 4)/(4) = (y + 2)/(5) = (z + 3)/(3) and (x - 1)/(3) = (y - 3)/(4) = (z - 4)/(2) is

JEE Main 2023 Solution View → 149

If the equation of the plane containing the line x + 2y + 3z - 4 = 0 = 2x + y - z + 5 and perpendicular to the plane → r = ( ^ i - ^ j ) + λ( ^ i + ^ j + ^ k ) + μ ( ^ i - 2 ^ j +

JEE Main 2023 Solution View → 150

Let λ _ 1 , λ _ 2 be the values of λ for which the points ((5)/(2), 1, λ) and (- 2, 0, 1) are at equal distance from the plane 2x + 3y - 6z + 7 If λ _ 1 > λ _ 2 then the distance

JEE Main 2023 Solution View → 151

Let the line L pass through the point ( 0, 1, 2 ) , intersect the line (x - 1)/(2) = (y - 2)/(3) = (z - 3)/(4) and be parallel to the plane 2x + y - 3z = 4 . Then the distance of

JEE Main 2023 Solution View → 152

A plane P contains the line of intersection of the plane → r · ( ^ i + ^ j + ^ k ) = 6 and → r · (2 ^ i + 3 ^ j + 4 ^ k ) = - 5 . If P passes through the point ( 0, 2, - 2 )

JEE Main 2023 Solution View → 153

If the lines (x - 1)/(2) = (2 - y)/(- 3) = (z - 3)/(α) and (x - 4)/(5) = (y - 1)/(2) = (z)/(β) intersect, then the magnitude of the minimum value of 8αβ is _____.

JEE Main 2023 Solution View → 154

One vertex of a rectangular parallelopiped is at the origin O and the lengths of its edges along x, y and z axes are 3, 4 and 5 units respectively. Let P be the vertex ( 3, 4, 5 )

JEE Main 2023 Solution View → 155

If the equation of the plane passing through the line of intersection of the planes 2x - y + z = 3, 4x - 3y + 5z + 9 = 0 and parallel to the line (x + 1)/(- 2) = (y + 3)/(4) = (z

JEE Main 2023 Solution View → 156

Let the image of the point P ( 1, 2, 3 ) in the plane 2x – y + z = 9 be Q . If the coordinates of the point R are ( 6, 10, 7 ) , then the square of the area of the triangle PQR is

JEE Main 2023 Solution View → 157

Let the plane P pass through the intersection of the planes 2x + 3y - z = 2 and x + 2y + 3z = 6 , and be perpendicular to the plane 2x + y - z + 1 = 0 . If d is the distance of P

JEE Main 2023 Solution View → 158

Let + + = 1 be the equation of a plane passing through the point (3, - 2, 5) and perpendicular to the line joining the points (1, 2, 3) and (- 2, 3, 5). Then the value of α is

JEE Main 2023 Solution View → 159

The point of intersection C of the plane 8x + y + 2z = 0 and the line joining the points A (- 3, - 6, 1) and B (2, 4, - 3) divides the line segment AB internally in the ratio k: 1

JEE Main 2023 Solution View → 160

Let the image of the point P(2, - 1, 3) in the plane x + 2y - z = 0 be Q . Then the distance of the plane 3x + 2y + z + 29 = 0 from the point Q is

JEE Main 2023 Solution View → 161

The shortest distance between the lines (x - 5)/(1) = (y - 2)/(2) = (z - 4)/(- 3) and (x + 3)/(1) = (y + 5)/(4) = (z - 1)/(- 5) is

JEE Main 2023 Solution View → 162

Let the plane P: 8x + α _ 1 y + α _ 2 z + 12 = 0 be parallel to the line L: (x + 2)/(2) = (y - 3)/(3) = (z + 4)/(5) . If the intercept of P on the y -axis is 1 , then the distance

JEE Main 2023 Solution View → 163

Let P be the plane, passing through the point (1, - 1, - 5) and perpendicular to the line joining the points (4, 1, - 3) and (2, 4, 3). Then the distance of P from the point (3

JEE Main 2023 Solution View → 164

The foot of perpendicular from the origin O to a plane P which meets the co-ordinate axes at the point A , B, C is ( 2, a, 4 ) , a ∈ N . If the volume of the tetrahedron OABC is

JEE Main 2023 Solution View → 165

Let the shortest distance between the lines L: (x - 5)/(- 2) = (y - λ)/(0) = (z + λ)/(1), λ ≥ 0 and L _ 1 : x + 1 = y - 1 = 4 - z be 2 6 . If ( α, β, γ ) lies on L , then which of

JEE Main 2023 Solution View → 166

Let the line L: (x - 1)/(2) = (y + 1)/(- 1) = (z - 3)/(1) intersect the plane 2x + y + 3z = 16 at the point P . Let the point Q be the foot of perpendicular from the point R(1

JEE Main 2023 Solution View → 167

Let θ be the angle between the planes P _ 1 = → r · ( ^ i + ^ j + 2 ^ k ) = 9 and P _ 2 = → r · (2 ^ i - ^ j + ^ k ) = 15 . Let L be the line that meets P _ 2 at the point (4

JEE Main 2023 Solution View → 168

A vector → v in the first octant is inclined to the x axis at 60 ° , to the y -axis at 45 ° and to the z -axis at an acute angle. If a plane passing through the points ( 2 , - 1

JEE Main 2023 Solution View → 169

If a plane passes through the points ( - 1, k, 0 ) , ( 2, k, - 1 ) , ( 1, 1, 2 ) and is parallel to the line (x - 1)/(1) = (2y + 1)/(2) = (z + 1)/(- 1) , then the value of k ^ 2 +

JEE Main 2023 Solution View → 170

Let a line L pass through the point P ( 2, 3, 1 ) and be parallel to the line x + 3y - 2z - 2 = 0 = x - y + 2z . If the distance of L from the point ( 5, 3, 8 ) is α , then 3 α ^

JEE Main 2023 Solution View → 171

The line l _ 1 passes through the point (2, 6, 2) and is perpendicular to the plane 2x + y - 2z = 10 . Then the shortest distance between the line l _ 1 and the line (x + 1)/(2) =

JEE Main 2023 Solution View → 172

Let a unit vector → OP make angle α, β, γ with the positive directions of the co-ordinate axes OX, OY , OZ respectively, where β ∈ (0, (π)/(2)) . → OP is perpendicular to the

JEE Main 2023 Solution View → 173

If the equation of the plane passing through the point ( 1, 1, 2 ) and perpendicular to the line x - 3y + 2z - 1 = 0 = 4x - y + z is Ax + By + Cz = 1 , then 140 ( C - B + A ) is

JEE Main 2023 Solution View → 174

If λ _ 1 < λ _ 2 are two values of λ such that the angle between the planes P _ 1 : → r ( 3 ^ i - 5 ^ j + ^ k ) = 7 and P _ 2 : → r · ( λ ^ i + ^ j - 3 ^ k ) = 9 is ^ - 1 ( 2 6 5

JEE Main 2023 Solution View → 175

Shortest distance between the lines (x - 1)/(2) = (y + 8)/(- 7) = (z - 4)/(5)and(x - 1)/(2) = (y - 2)/(1) = (z - 6)/(- 3)is

JEE Main 2023 Solution View → 176

The plane 2 x-y+z=4 intersects the line segment joining the points A(a,-2,4) and B(2, ~b,-3) at the point C in the ratio 2: 1 and the distance of the point C from the origin is 5

JEE Main 2023 Solution View → 177

If the lines (x - 1)/(1) = (y - 2)/(2) = (z + 3)/(1) and (x - a)/(2) = (y + 2)/(3) = (z - 3)/(1) intersects at the point P , then the distance of the point P from the plane z = a

JEE Main 2023 Solution View → 178

Let the equation of the plane P containing the line x + 10 = (8 - y)/(2) = z be ax + by + 3z = 2 ( a + b ) and the distance of the plane P from the point ( 1, 27, 7 ) be c . Then

JEE Main 2023 Solution View → 179

Let the co-ordinates of one vertex of ∆ ABC be A ( 0, 2, α ) and the other two vertices lie on the line (x + α)/(5) = (y - 1)/(2) = (z + 4)/(3) . For α ∈ ℤ , if the area of ∆ ABC

JEE Main 2023 Solution View → 180

The shortest distance between the lines x + 1 = 2y = - 12z and x = y + 2 = 6z - 6 is

JEE Main 2023 Solution View → 181

The foot of perpendicular of the point (2, 0, 5) on the line (x + 1)/(2) = (y - 1)/(5) = (z + 1)/(- 1) is (α, β, γ) . Then. Which of the following is NOT correct?

JEE Main 2023 Solution View → 182

If the shortest distance between the line joining the points (1, 2, 3) and (2, 3, 4) , and the line (x - 1)/(2) = (y + 1)/(- 1) = (z - 2)/(0) is α , then 28 α ^ 2 is equal to

JEE Main 2023 Solution View → 183

The distance of the point P(4, 6, - 2) from the line passing through the point (- 3, 2, 3) and parallel to a line with direction ratios 3, 3, - 1 is equal to:

JEE Main 2023 Solution View → 184

Consider the lines L _ 1 and L _ 2 given by L _ 1 : (x - 1)/(2) = (y - 3)/(1) = (z - 2)/(2) L _ 2 : (x - 2)/(1) = (y - 2)/(2) = (z - 3)/(3) A line L _ 3 having direction ratios 1

JEE Main 2023 Solution View → 185

Let the equation of the plane passing through the line x - 2y - z - 5 = 0 = x + y + 3z - 5 and parallel to the line x + y + 2z - 7 = 0 = 2x + 3y + z - 2 be ax + by + cz = 65 .

JEE Main 2023 Solution View → 186

Let the plane containing the line of intersection of the planes P _ 1 : x + (λ + 4)y + z = 1 and P _ 2 : 2x + y + z = 2 pass through the points (0, 1, 0) and (1, 0, 1) . Then the

JEE Main 2023 Solution View → 187

If the foot of the perpendicular drawn from (1, 9, 7) to the line passing through the point (3, 2, 1) and parallel the planes x + 2y + z = 0 and 3y - z = 3 is (α, β, γ) , then α +

JEE Main 2023 Solution View → 188

If the shortest distance between the lines x + 6 2 = y - 6 3 = z - 6 4 and (x - λ)/(3) = y - 2 6 4 = z + 2 6 5 is 6 , then sum of squares of all possible values(s) of λ is

JEE Main 2023 Solution View → 189

The distance of the point (7, - 3, - 4) from the plane containing the points (2, - 3, 1), (- 1, 1, - 2) and (3, - 4, 2) is equal to:

JEE Main 2023 Solution View → 190

Let P _ 1 and P _ 2 be two planes given by P _ 1 : 10x + 15y + 12z - 60 = 0, P _ 2 : - 2x + 5y + 4z - 20 = 0 . Which of the following straight lines can be an edge of some

JEE Advanced 2022 Solution View → 191

Let S be the reflection of a point Q with respect to the plane given by → r = - (t + p) ^ i + t ^ j + (1 + p) ^ k where t, p are real parameters and ^ i , ^ j , ^ k are the unit

JEE Advanced 2022 Solution View → 192

Let α, β, γ, δ be real numbers such that α ^ 2 + β ^ 2 + γ ^ 2 ≠ 0 and α + γ = 1 . Suppose the point (3, 2, - 1) is the mirror image of the point (1, 0, - 1) with respect to the

JEE Advanced 2020 Solution View → 193

Let L _ 1 and L _ 2 be the following straight lines. L _ 1 : (x - 1)/(1) = (y)/(- 1) = (z - 1)/(3) and L _ 2 : (x - 1)/(- 3) = (y)/(- 1) = (z - 1)/(1) Suppose the straight line L

JEE Advanced 2020 Solution View → 194

Three lines L _ 1 : → r = λ ^ i , λ ∈ R, L _ 2 : → r = ^ k + μ ^ j , μ ∈ R and L _ 3 : → r = ^ i + ^ j + ν ^ k , ν ∈ R are given. For which point(s) Q and L _ 2 can we find a

JEE Advanced 2019 Solution View → 195

Let L _ 1 and L _ 2 denotes the lines → r = ^ i + λ(- ^ i + 2 ^ j + 2 ^ k ), λ ∈ R and → r = μ(2 ^ i - ^ j + 2 ^ k ), μ ∈ R respectively. If L _ 3 is a line which is perpendicular

JEE Advanced 2019 Solution View → 196

Three lines are given by → r = λ ^ i , λ ∈ R → r = μ( ^ i + ^ j ), μ ∈ R and → r = ν( ^ i + ^ j + ^ k ), ν ∈ R . Let the lines cut the plane x + y + z = 1 at the points A, B and C

JEE Advanced 2019 Solution View → 197

Let P be a point in the first octant, whose image Q in the plane x + y = 3 (that is, the line segment PQ is perpendicular to the plane x + y = 3 and the mid-point of PQ lies in

JEE Advanced 2018 Solution View → 198

Let P _ 1 : 2x + y - z = 3and P _ 2 : x + 2y + z = 2 be two planes. Then, which of the following statement(s) is (are) TRUE?

JEE Advanced 2018 Solution View → 199

The equation of the plane passing through the point ( 1,1, 1 ) and perpendicular to the planes 2x + y - 2z = 5 and 3x - 6y - 2z = 7 is

JEE Advanced 2017 Solution View → 200

Let P be the image of the point ( 3, 1, 7 ) with respect to the plane x - y + z = 3 . Then the equation of the plane passing through P and containing the straight line (x)/(1) =

JEE Advanced 2016 Solution View →
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Related JEE Mathematics chapters

Application of Derivatives (795)Sequences and Series (748)Functions (700)Definite Integration (692)Vector Algebra (616)Differential Equations (586)Continuity and Differentiability (576)Probability (561)Complex Number (551)Binomial Theorem (550)Quadratic Equation (517)Determinants (508)

Three Dimensional Geometry in other exams

NDA Three Dimensional Geometry (176)BITSAT Three Dimensional Geometry (40)