Quantrex Academy Quantrex AcademyPYQs with solutions · JEE · NEET · NDA

Home · NDA PYQs · Mathematics · Three Dimensional Geometry

NDA Three Dimensional Geometry PYQs with Solutions

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

176 questionsMathematics2010–2026Answers + solutions

About Three Dimensional Geometry PYQs

Three Dimensional Geometry has 176 previous year questions in the Quantrex Academy NDA Mathematics bank. The 176 questions in this list come from NDA (176), spanning 2010 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: 6
  • 2025: 10
  • 2024: 12
  • 2023: 12
  • 2022: 9
  • 2021: 10
  • 2020: 6
  • 2019: 10
  • 2018: 8
  • 2017: 11
  • 2016: 7
  • 2015: 13

Three Dimensional Geometry questions with solutions

1

Passage: The equation of the sphere S is x^2+y^2+z^2-4x-6y-12z+k=0 . Question: If the radius of the sphere S is 8 units, what is the value of k ?

NDA 2026 Solution View → 2

Passage: A line L passing through the point (-1,2,-3) is perpendicular to the plane P given by 2x+3y+z+5=0 . Question: What is the equation of the line L ?

NDA 2026 Solution View → 3

Passage: P(-2,-3,5) , Q(4,-1,5) , R(6,-4,8) and S(2,-6,10) are four points. Question: Consider the following statements : I. PQ is parallel to RS . II. PR is perpendicular to QS .

NDA 2026 Solution View → 4

Passage: A line L passing through the point (-1,2,-3) is perpendicular to the plane P given by 2x+3y+z+5=0 . Question: What are the direction ratios of a line M parallel to the

NDA 2026 Solution View → 5

Passage: P(-2,-3,5) , Q(4,-1,5) , R(6,-4,8) and S(2,-6,10) are four points. Question: What is (PQ^2+2QS^2-2PR^2) equal to ?

NDA 2026 Solution View → 6

Passage: The equation of the sphere S is x^2+y^2+z^2-4x-6y-12z+k=0 . Question: What is the radius of the sphere passing through origin and concentric with the sphere S ?

NDA 2026 Solution View → 7

For the following two (02) items: A plane P is parallel to the line having direction ratios 1, 3, 2 and contains the line of intersection of the planes 6x + 4y - 5z = 2 and x - 2y

NDA 2025 Solution View → 8

For the following two (02) items: Suppose S is the sphere with the smallest radius that passes through the points A(1, 0, 0) , B(0, 1, 0) and C(0, 0, 1) . On which one of the

NDA 2025 Solution View → 9

A(1, 2, -1) , B(2, 5, -2) and C(4, 4, -3) are three vertices of a rectangle. What is the area of the rectangle?

NDA 2025 Solution View → 10

If a line (x+1)/(p) = (y-1)/(q) = (z-2)/(r) where p = 2q = 3r , makes an angle θ with the positive direction of y -axis, then what is 2θ equal to?

NDA 2025 Solution View → 11

What is the equation of the plane passing through the point (1, 1, 1) and perpendicular to the line whose direction ratios are 3, 2, 1 ?

NDA 2025 Solution View → 12

For the following two (02) items: Let A(1, -1, 0) , B(-2, 1, 8) and C(-1, 2, 7) are three consecutive vertices of a parallelogram ABCD . What is the fourth vertex D ?

NDA 2025 Solution View → 13

For the following two (02) items: Suppose S is the sphere with the smallest radius that passes through the points A(1, 0, 0) , B(0, 1, 0) and C(0, 0, 1) . What is the radius of S ?

NDA 2025 Solution View → 14

If a line in 3 dimensions makes angles α , β and γ with the positive directions of the coordinate axes, then what is (α+β) (α-β) equal to?

NDA 2025 Solution View → 15

A line makes angles α , β and γ with the positive directions of the coordinate axes. If a = ( ^2α) i + ( ^2β) j + ( ^2γ) k and b = i + j + k , then what is a · b equal to?

NDA 2025 Solution View → 16

For the following two (02) items: A plane P is parallel to the line having direction ratios 1, 3, 2 and contains the line of intersection of the planes 6x + 4y - 5z = 2 and x - 2y

NDA 2025 Solution View → 17

Paragraph: Let 2 x^2+2 y^2+2 z^2+3 x+3 y+3 z-6=0 be a sphere. Question: What is the diameter of the sphere?

NDA 2024 Solution View → 18

Paragraph: Let S be the line of intersection of two planes x+y+z=1 and 2 x+3 y-4 z=8 . Question: Which of the following are the direction ratios of S ?

NDA 2024 Solution View → 19

Paragraph: Let S be the line of intersection of two planes x+y+z=1 and 2 x+3 y-4 z=8 . Question: If (l, m, n) are direction cosines of S, then what is the value of 43 (l²-m²-n²) ?

NDA 2024 Solution View → 20

Paragraph: Let L: x+y+z+4=0=2 x-y-z+8 be a line and P: x+2 y+3 z+1=0 be a plane Question: What is the point of intersection of L and P ?

NDA 2024 Solution View → 21

If (1,-1,2) and (2,1,-1) are the end points of a diameter of a sphere x^2+y^2+z^2+2 u x+2 v y+2 w z-1=0 , then what is u+v+w equal to?

NDA 2024 Solution View → 22

If l, m, n > are the direction cosines of a normal to the plane 2 x-3 y+6 z+4=0 , then what is the value of 49 (7 l²+m²-n²) ?

NDA 2024 Solution View → 23

If p is the perpendicular distance from origin to the plane passing through (1,0,0),(0,1,0) and (0,0,1) , then what is 3 p^2 equal to?

NDA 2024 Solution View → 24

A line through (1,-1,2) with direction ratios meets the plane x+2 y+3 z=18 . What is the point of intersection of line and plane?

NDA 2024 Solution View → 25

Paragraph: Let 2 x^2+2 y^2+2 z^2+3 x+3 y+3 z-6=0 be a sphere. Question: The centre of the sphere lies on the plane

NDA 2024 Solution View → 26

Paragraph: Let L: x+y+z+4=0=2 x-y-z+8 be a line and P : x+2 y+3 z+1=0 be a plane Question: What are the direction ratios of the line?

NDA 2024 Solution View → 27

If a direction cosines of a line are connected by relation l+2 m+n=0,2 l-2 m+3 n=0 , then what is the value of l^2+m^2-n^2 ?

NDA 2024 Solution View → 28

If a vector of magnitude 2 units makes an angle (π)/(3) with 2 i , (π)/(4) with 3 j and an acute angle θ with 4 k , then what are the components of the vector?

NDA 2024 Solution View → 29

If L is the line with DIRECTIONS ratios and passing through (1,-1,1) , then what are the coordinates of the points on L whose distance from (1,-1,1) is 2 units?

NDA 2023 Solution View → 30

Which one of the planes is parallel to the line (x-2)/(3)=(y-3)/(4)=(z-4)/(5) ?

NDA 2023 Solution View → 31

What is the equation of the sphere concentric with the sphere x^2+y^2+z^2-2 x-6 y-8 z-5=0 and which passes through the origin?

NDA 2023 Solution View → 32

Paragraph: Let A(1,-1,2) and B(2,1,-1) be the end points of the diameter of the sphere x^2+y^2+z^2+2 u x+2 v y+2 w z-1=0 Question: What is u+v+w equal to?

NDA 2023 Solution View → 33

Paragraph: Let A(1,-1,2) and B(2,1,-1) be the end points of the diameter of the sphere x^2+y^2+z^2+2 u x+2 v y+2 w z-1=0 Question: If P(x, y, z) is any point on the sphere, then

NDA 2023 Solution View → 34

A point P lies on the line joining A(1,2,3) and B(2,10,1) . If z -coordinate of P is 7 , what is the sum of other two coordinates?

NDA 2023 Solution View → 35

Paragraph: Consider two lines whose direction ratios are (2,-1,2) and (k, 3,5) . They are inclined at an angle (π)/(4) . Question: What is the value of k ?

NDA 2023 Solution View → 36

Paragraph: Consider two lines whose direction ratios are (2,-1,2) and (k, 3,5) . They are inclined at an angle (π)/(4) . Question: What are the direction ratios of a line which is

NDA 2023 Solution View → 37

Paragraph: The position vectors of two points A and B are i - j and j + k respectively. Question: Consider the following points: 1. (-1,-3,1) 2. (-1,3,2) 3. (-2,5,3) Which of the

NDA 2023 Solution View → 38

Paragraph: Let a vector a =4 i -8 j +k make angles α, β, γ with the positive directions of x, y, z axes respectivelv, Question: What is α equal to?

NDA 2023 Solution View → 39

What is the angle between the lines 2 x=3 y=-z and 6 x=-y=-4 z ?

NDA 2023 Solution View → 40

Paragraph: Let a vector a =4 i -8 j + k make angles α, β, γ with the positive directions of x, y, z axes respectively. Question: What is 2 β+ 2 γ equal to?

NDA 2023 Solution View → 41

Consider the equation of a sphere x^2+y^2+z^2-4 x-6 y-8 z-16=0 . Which of the following statements is/are correct? 1. z -axis is tangent to the sphere. 2. The centre of the sphere

NDA 2022 Solution View → 42

A plane cuts intercepts 2,2,1 on the coordinate axes. What are the direction cosines of the normal to the plane?

NDA 2022 Solution View → 43

Consider the following statements : 1. The direction ratios of y -axis can be 2. The direction ratios of a line perpendicular to z -axis can be 5,6,0 Which of the statements given

NDA 2022 Solution View → 44

The plane 6 x+k y+3 z-12=0 where meets the coordinate axes at A, B and C respectively. The equation of the sphere passing through the origin and A, B, C is x^2+y^2+z^2-2 x-3 y-4

NDA 2022 Solution View → 45

The plane 6 x+k y+3 z-12=0 where meets the coordinate axes at A, B and C respectively. The equation of the sphere passing through the origin and A, B, C is x^2+y^2+z^2-2 x-3 y-4

NDA 2022 Solution View → 46

Let the plane (2 x)/(k)+(2 y)/(3)+(z)/(3)=2 pass through the point (2,3,-6) . What are the direction ratios of a normal to the plane?

NDA 2022 Solution View → 47

Let the plane (2 x)/(k)+(2 y)/(3)+(z)/(3)=2 pass through the point (2,3,-6) . If p, q and r are the intercepts made by the plane on the coordinate axes respectively, then what is

NDA 2022 Solution View → 48

Consider the points A(2,4,6), B(-2,-4,-2), C(4,6,4) and D(8,14,12) . Which of the following statements is/ are correct? 1. The points are the vertices of a rectangle A B C D . 2.

NDA 2022 Solution View → 49

The plane 6 x+k y+3 z-12=0 where meets the coordinate axes at A, B and C respectively. The equation of the sphere passing through the origin and A, B, C is x^2+y^2+z^2-2 x-3 y-4

NDA 2022 Solution View → 50

The locus of a point P(x, y, z) which moves in such a way that z=7 is a

NDA 2021 Solution View → 51

Consider the following statements : 1. A line in space can have infinitely many direction ratios. 2. It is possible for certain line that the sum of the squares of direction

NDA 2021 Solution View → 52

The x y -plane divides the line segment joining the points (-1,3,4) and (2,-5,6)

NDA 2021 Solution View → 53

A B C D E F G H is a cuboid with base A B C D . Let A(0,0,0), B(12,0,0), C(12,6,0) and G(12,6,4) be the vertices. If α is the angle between A B and A G ; β is the angle between A

NDA 2021 Solution View → 54

The number of spheres of radius r touching the coordinate axes is

NDA 2021 Solution View → 55

What is the angle between the two lines having direction ratios (6,3,6) and (3,3,0) ?

NDA 2021 Solution View → 56

If l, m, n are the direction cosines of the line x-1=2(y+3)=1-z , then what is l^4+m^4+n^4 equal to?

NDA 2021 Solution View → 57

What is the projection of the line segment joining A(1,7,-5) and B(-3,4,-2) on y -axis?

NDA 2021 Solution View → 58

What is the number of possible values of k for which the line joining the points (k, 1,3) and (1,-2, k+1) also passes through the point (15,2,-4) ?

NDA 2021 Solution View → 59

The foot of the perpendicular drawn from the origin to the plane x+y+z=3 is

NDA 2021 Solution View → 60

If a line has direction ratios , then what is the sum of the squares of its direction cosines?

NDA 2020 Solution View → 61

Into how many compartments do the coordinate planes divide the space?

NDA 2020 Solution View → 62

Let A be a point in space such that | O A |=12 , where O is the origin. If O A is inclined at angles 45^ ^ ∘ and 60^ ^ ∘ with x axis and y -axis respectively, then what is O A

NDA 2020 Solution View → 63

What is the equation of the plane which cuts an intercept 5 units on the z -axis and is parallel to x y -plane?

NDA 2020 Solution View → 64

What is the length of the diameter of the sphere whose centre is at (1,-2,3) and which touches the plane 6 x-3 y+2 z-4=0 ?

NDA 2020 Solution View → 65

What is the perpendicular distance from the point (2,3,4) to the line (x-0)/(1)=(y-0)/(0)=(z-0)/(0) ?

NDA 2020 Solution View → 66

A point on a line has coordinates (p+1, p-3, 2 p) where p is any real number. What are the direction cosines of the line?

NDA 2019 Solution View → 67

A straight line passes through the point (1,1,1) makes an angle 60^ ^ ∘ with the positive direction of z -axis, and the cosine of the angles made by it with the positive

NDA 2019 Solution View → 68

If the line (x-4)/(1)=(y-2)/(1)=(z-k)/(2) lies on the plane 2 x-4 y+z=7 , then what is the value of k ?

NDA 2019 Solution View → 69

The equation of the plane passing through the intersection of the planes 2 x+y+2 z=9,4 x-5 y-4 z=1 and the point (3,2,1) is

NDA 2019 Solution View → 70

If the points (x, y,-3),(2,0,-1) and (4,2,3) lie on a straight line, then what are the values of x and y respectively?

NDA 2019 Solution View → 71

The distance between the parallel planes 4 x-2 y+4 z+9=0 and 8 x-4 y+8 z+21=0 is

NDA 2019 Solution View → 72

What are the direction cosines of z -axis?

NDA 2019 Solution View → 73

If the position vectors of points A and B are 3 i -2 j + k and 2 i +4 j -3 k respectively, then what is the length of A B ?

NDA 2019 Solution View → 74

A point on the line (x-1)/(1)=(y-3)/(2)=(z+2)/(7) has coordinates

NDA 2019 Solution View → 75

What is the radius of the sphere x^2+y^2+z^2-6 x+8 y-10 z+1=0 ?

NDA 2019 Solution View → 76

Coordinates of the points O, P, Q and R are respectively (0,0,0),(4,6,2 m),(2,0,2 n) and (2,4,6) . Let L, M, N and K be points on the sides O R, O P, P Q and Q R respectively such

NDA 2018 Solution View → 77

Consider the following statements: 1. The angle between the planes 2 x-y+z=1 and x+y+2 z=3 is (π)/(3) 2. The distance between the planes 6 x-3 y+6 z+2=0 and 2 x-y+2 z+4=0 is

NDA 2018 Solution View → 78

Let the coordinates of the points A, B, C be (1,8,4) , (0,-11,4) and (2,-3,1) respectively. What are the coordinates of the point D which is the foot of the perpendicular from A

NDA 2018 Solution View → 79

What is the equation of the plane passing through the points (-2,6,-6),(-3,10,-9) and (-5,0,-6) ?

NDA 2018 Solution View → 80

A sphere of constant radius r through the origin intersects the coordinate axes in A, B and C. What is the locus of the centroid of the triangle ABC ?

NDA 2018 Solution View → 81

What is the distance of the point (2,3,4) from the plane 3 x-6 y+2 z+11=?

NDA 2018 Solution View → 82

The line (x-1)/(2)-(y-2)/(3)=(z-3)/(3) is given by

NDA 2018 Solution View → 83

What is the equation to the sphere whose centre is at (-2,3,4) and radius is 6 units?

NDA 2018 Solution View → 84

The length of the normal from origin to the plane x+2 y-2 z=9 is equal to

NDA 2017 Solution View → 85

If α, β and γ are the angles which the vector OP (O being the origin) makes with positive direction of the coordinate axes, then which of the following are correct? 1. ^2 α+ ^2 β=

NDA 2017 Solution View → 86

The point of intersection of the line joining the points (-3,4,-8) and (5,-6,4) with the XY-plane is

NDA 2017 Solution View → 87

If the angle between the lines whose direction ratios are (2,-1,2) and (x, 3,5) is (π)/(4) , then the smaller value of x is

NDA 2017 Solution View → 88

A straight line with direction cosines (0,1,0) is

NDA 2017 Solution View → 89

A variable plane passes through a fixed point (a, b, c) and cuts the axes in A, B and C respectively. The locus of the centre of the sphere OABC, O being the origin, is

NDA 2017 Solution View → 90

The line passing through the points (1,2,-1) and (3,-1,2) meets the yz-plane at which one of the following points?

NDA 2017 Solution View → 91

(0,0,0),(a, 0,0),(0, b, 0) and (0,0, c) are four distinct points. What are the coordinates of the point which is equidistant from the four points?

NDA 2017 Solution View → 92

Under which one of the following conditions are the lines x=ay+b ; z=cy+d and x=ey+f ; z=gy+h perpendicular?

NDA 2017 Solution View → 93

The equation of the plane passing through the line of intersection of the planes x+y+z=1,2 x+3 y+4 z=7 , and perpendicular to the plane x-5 y+3 z=5 is given by

NDA 2017 Solution View → 94

The points P(3,2,4), Q(4,5,2), R(5,8,0) and S(2,-1,6) are

NDA 2017 Solution View → 95

Paragraph: Let Q be the image of the point P(-2,1,-5) in the plane 3 x-2 y+2 z+1=0 . Question: Consider the following: 1. The direction ratios of the line segment PQ are . 2. The

NDA 2016 Solution View → 96

Paragraph: A line L passes through the point P(5,-6,7) and is parallel to the planes x+y+z=1 and 2 x-y-2 z=3 . Question: What are the direction ratios of the line of intersection

NDA 2016 Solution View → 97

Paragraph: A line L passes through the point P(5,-6,7) and is parallel to the planes x+y+z=1 and 2 x-y-2 z=3 . Question: What is the equation of the line L ?

NDA 2016 Solution View → 98

Paragraph: Let Q be the image of the point P(-2,1,-5) in the plane 3 x-2 y+2 z+1=0 . Question: Consider the following: 1. The coordinates of Q are (4,-3,-1) . 2. PQ is of length

NDA 2016 Solution View → 99

A plane P passes through the line of intersection of the planes 2 x-y+3 z=2, x+y-z=1 and the point (1,0,1) . If the plane P touches the sphere x^2+y^2+z^2=r^2 , then what is r

NDA 2016 Solution View → 100

A plane P passes through the line of intersection of the planes 2 x-y+3 z=2, x+y-z=1 and the point (1,0,1) . What is the equation of the plane P?

NDA 2016 Solution View → 101

A plane P passes through the line of intersection of the planes 2 x-y+3 z=2, x+y-z=1 and the point (1,0,1) . What are the direction ratios of the line of intersection of the given

NDA 2016 Solution View → 102

The lines 2 x=3 y=-z and 6 x=-y=-4 z

NDA 2015 Solution View → 103

What are the co-ordinates of the foot of the perpendicular drawn from the point (3,5,4) on the plane z=0 ?

NDA 2015 Solution View → 104

The radius of the sphere 3 x^2+3 y^2+3 z^2-8 x+4 y+8 z-15=0 is

NDA 2015 Solution View → 105

The projections of a directed line segment on the coordinate axes are 12, 4, 3 respectively. What are the direction cosines of the line segment?

NDA 2015 Solution View → 106

The projections of a directed line segment on the coordinate axes are 12, 4, 3 respectively. What is the length of the line segment?

NDA 2015 Solution View → 107

From the point P(3,-1,11) , a perpendicular is drawn on the line L given by the equation (x)/(2)=(y-2)/(3)=(z-3)/(4) . Let Q be the foot of the perpendicular. What are the

NDA 2015 Solution View → 108

A point P(1,2,3) is one vertex of a cuboid formed by the coordinate planes and the planes passing through P and parallel to the coordinate planes. What is the length of one of the

NDA 2015 Solution View → 109

From the point P(3,-1,11) , a perpendicular is drawn on the line L given by the equation (x)/(2)=(y-2)/(3)=(z-3)/(4) . Let Q be the foot of the perpendicular. What is the length

NDA 2015 Solution View → 110

The lengths of the intercepts on the co-ordinate axes made by the plane 5 x+2 y+z-13=0 are

NDA 2015 Solution View → 111

Let α, β, γ be distinct real numbers. The points with position vectors α i +β j +γ k , β i +γ j +α k and γ i +α j +β k

NDA 2015 Solution View → 112

The direction ratios of the line perpendicular to the lines with direction ratios and are

NDA 2015 Solution View → 113

A triangular plane ABC with centroid (1, 2, 3) cuts the coordinate axes at A, B, C respectively. What is the equation of plane ABC?

NDA 2015 Solution View → 114

A point P(1,2,3) is one vertex of a cuboid formed by the coordinate planes and the planes passing through P and parallel to the coordinate planes. What is the equation of the

NDA 2015 Solution View → 115

Consider a sphere passing through the origin and the points (2,1,-1),(1,5,-4),(-2,4,-6) . What is the centre of the sphere?

NDA 2014 Solution View → 116

Consider a sphere passing through the origin and the points (2,1,-1),(1,5,-4),(-2,4,-6) . Consider the following statements: 1. The sphere passes through the point (0,4,0) . 2.

NDA 2014 Solution View → 117

The line joining the points (2,1,3) and (4,-2,5) cuts the plane 2 x+y-z=3 . What is the ratio in which the plane divides the line?

NDA 2014 Solution View → 118

Consider the plane passing through the points A(2,2,1), B(3,4,2) and C(7,0,6) . What are the direction ratios of the normal to the plane?

NDA 2014 Solution View → 119

Paragraph : A straight line passes through (1,-2,3) and perpendicular to the plane 2 x+3 y-z=7 . Question : Where does the line meet the plane?

NDA 2014 Solution View → 120

Paragraph : A straight line passes through (1,-2,3) and perpendicular to the plane 2 x+3 y-z=7 . Question : What are the direction ratios of normal to plane?

NDA 2014 Solution View → 121

Paragraph : Consider the spheres x^2+y^2+z^2-4 y+3=0 and x^2+y^2+z^2+2 x+4 z-4=0 . Question : Consider the following statements: 1. The two spheres intersect each other. 2. The

NDA 2014 Solution View → 122

Paragraph : A straight line passes through (1,-2,3) and perpendicular to the plane 2 x+3 y-z=7 . Question : What is the image of the point (1,-2,3) in the plane?

NDA 2014 Solution View → 123

Paragraph : The vertices of a triangle A B C are A(2,3,1), B(-2,2,0) and C(0,1,-1) . Question : What is the cosine of angle ABC ?

NDA 2014 Solution View → 124

Paragraph : The vertices of a triangle A B C are A(2,3,1), B(-2,2,0) and C(0,1,-1) . Question : What is the magnitude of the line joining mid points of the sides AC and BC ?

NDA 2014 Solution View → 125

Paragraph : Let a vector r make angles 60^ ^ ∘ , 30^ ^ ∘ with x and y -axis respectively. Question : What angle does r make with z -axis?

NDA 2014 Solution View → 126

Paragraph : The vertices of a triangle A B C are A(2,3,1), B(-2,2,0) and C(0,1,-1) . Question : What is the area of the triangle?

NDA 2014 Solution View → 127

Paragraph : Let a vector r make angles 60^ ^ ∘ , 30^ ^ ∘ with x and y -axis respectively. Question : What are the direction cosines of r ?

NDA 2014 Solution View → 128

A line passes through the points (6,-7,-1) and (2,-3,1) . What are the direction ratios of the line?

NDA 2014 Solution View → 129

Consider a sphere passing through the origin and the points (2,1,-1),(1,5,-4),(-2,4,-6) . What is the radius of the sphere?

NDA 2014 Solution View → 130

Consider the plane passing through the points A(2,2,1), B(3,4,2) and C(7,0,6) . Which one of the following points lies on the plane?

NDA 2014 Solution View → 131

Paragraph : Consider the spheres x^2+y^2+z^2-4 y+3=0 and x^2+y^2+z^2+2 x+4 z-4=0 . Question : What is the distance between the centres of the two spheres?

NDA 2014 Solution View → 132

The line joining the points (2,1,3) and (4,-2,5) cuts the plane 2 x+y-z=3 . Where does the line cut the plane?

NDA 2014 Solution View → 133

What is the distance of the line 2 x+y+2 z=3 from the origin?

NDA 2013 Solution View → 134

What is the sum of the squares of direction cosines of x -axis?

NDA 2013 Solution View → 135

If the projections of a straight line segment on the coordinate axes are 2,3,6 , then the length of the segment is

NDA 2013 Solution View → 136

The sum of the direction cosines of z -axis is

NDA 2013 Solution View → 137

What is the distance between the planes x-2 y+z-1=0 and -3 x+6 y-3 z+2=0 ?

NDA 2013 Solution View → 138

What should be the value of k for which the equation 3 x^2+3 y^2+(k+1) z^2+x-y+z=0 represents the sphere?

NDA 2013 Solution View → 139

What is the angle between the planes 2 x-y-2 z+1=0 and 3 x-4 y+5 z-3=0 ?

NDA 2013 Solution View → 140

If the straight line (x-x_0)/(ℓ)=(y-y_0)/(m)=(z-z_0)/(n) is parallel to the plane a x+b y+c z+d=0 then which one of the following is correct?

NDA 2013 Solution View → 141

If θ is the acute angle between the diagonals of a cube, then which one of the following is correct?

NDA 2013 Solution View → 142

What is the equation of the sphere with unit radius having centre at the origin?

NDA 2013 Solution View → 143

If a line makes 30^ ^ ∘ with the positive direction of x -axis, angle β with the positive direction of y -axis and angle γ with the positive direction of z -axis, then what is ^2

NDA 2013 Solution View → 144

If a line OP of length r (where ' O ' is the origin) makes an angle α with x -axis and lies in the x z -plane, then what are the coordinates of P ?

NDA 2012 Solution View → 145

If the distance between the point (7,1,-3) and (4,5, λ) is 13 units, then what is one of the values of λ ?

NDA 2012 Solution View → 146

What is the angle between the lines (x-2)/(1)=(y+1)/(-2)=(z+2)/(1) and (x-1)/(1)=(2 y+3)/(3)=(z+5)/(2) ?

NDA 2012 Solution View → 147

What is the distance of the point (1,2,0) from y z plane is :

NDA 2012 Solution View → 148

What is the equation to the plane through (1,2,3) parallel to 3 x+4 y-5 z=0 ?

NDA 2012 Solution View → 149

What is the cosine of angle between the planes x+y+z+1=0 and 2 x-2 y+2 z+1=0 ?

NDA 2012 Solution View → 150

What is the diameter of the sphere x^2+y^2+z^2-4 x+6 y-8 z-7=0

NDA 2012 Solution View → 151

If a line makes the angles α, β, γ with the axes, then what is the value of 1+ 2 α+ 2 β+ 2 γ equal to?

NDA 2012 Solution View → 152

What are the direction ratios of normal to the plane 2 x-y+2 z+1=0 ?

NDA 2012 Solution View → 153

What are the direction cosines of a line which is equally inclined to the positive directions of the axes?

NDA 2012 Solution View → 154

What are the direction ratios of the line of intersection of the planes x=3 z+4 and y=2 z-3 ?

NDA 2012 Solution View → 155

What is the equation to the straight line passing through (a, b, c) and parallel to z -axis?

NDA 2012 Solution View → 156

What is the sum of the squares of direction cosines of the line joining the points (1,2,-3) and (-2,3,1) ?

NDA 2012 Solution View → 157

What is the locus of points of intersection of a sphere and a plane?

NDA 2011 Solution View → 158

What is the angle between two planes 2 x-y+z=4 and x+y+2 z=6 ?

NDA 2011 Solution View → 159

The equation to sphere passing through origin and the points (-1,0,0),(0,-2,0) and (0,0,-3) is x^2+y^2+z^2+f(x, y, z)=0 . What is f(x, y, z) equal to?

NDA 2011 Solution View → 160

What is the angle between the lines whose direction cosines are proportional to (2,3,4) and (1,-2,1) respectively?

NDA 2011 Solution View → 161

What is the radius of the sphere x^2+y^2+z^2-x-y-z=0 ?

NDA 2011 Solution View → 162

Which one of the following points lies on the plane 2 x+3 y-6 z=21 ?

NDA 2011 Solution View → 163

What is the acute angle between the planes x+y+2 z=3 and -2 x+y-z=11 ?

NDA 2011 Solution View → 164

Consider the following relations among the angles α , β, γ made by a vectors with the coordinate axes: 1. 2 α+ 2 β+ 2 γ=-1 2. ^2 α+ ^2 β+ ^2 γ=1 Which of the above is/are correct?

NDA 2011 Solution View → 165

What is the equation of the plane passing through the point (1,-1,-1) and perpendicular to each of the planes x-2 y-8 z=0 and 2 x+5 y-z=0 ?

NDA 2011 Solution View → 166

The two planes a x+b y+c z+d=0 and a x+b y+c z+d_1=0 , where d ≠ d_1 , have

NDA 2010 Solution View → 167

What is the distance of the origin from the plane 2 x+6 y-3 z+7=0 ?

NDA 2010 Solution View → 168

If the line through the points A(k, 1,-1) and B(2 k, 0,2) is perpendicular to the line through the points B and C(2+2 k, k, 1) , then what is the value of k ?

NDA 2010 Solution View → 169

The planes p x+2 y+2 z-3=0 and 2 x-y+z+2=0 intersect at an angle π / 4 . What is the value of p^2 ?

NDA 2010 Solution View → 170

What is the equation of the plane through z -axis and parallel to the line (x-1)/( θ)=(y+2)/( θ)=(z-3)/(0)

NDA 2010 Solution View → 171

Let O(0,0,0), P(3,4,5), Q(m, n, r) and R(1,1,1) be the vertices of a parallelogram taken in order. What is the value of m+n+r ?

NDA 2010 Solution View → 172

The vertices of a cube are (0,0,0),(2,0,0),(0,2,0) , (0,0,2),(2,2,0),(2,0,2),(0,2,2),(2,2,2) respectively. What is the angle between any two diagonals of the cube?

NDA 2010 Solution View → 173

The vertices of a cube are (0,0,0),(2,0,0),(0,2,0) , (0,0,2),(2,2,0),(2,0,2),(0,2,2),(2,2,2) respectively. What is the angle between one of the edges of the cube and the diagonal

NDA 2010 Solution View → 174

What is the area of the triangle with vertices (0,2,2) , (2,0,-1) and (3,4,0) ?

NDA 2010 Solution View → 175

Under what condition do the planes b x-a y=n, c y-b z=l, a z-c x=m intersect in a line?

NDA 2010 Solution View → 176

The vertices of a cube are (0,0,0),(2,0,0),(0,2,0) , (0,0,2),(2,2,0),(2,0,2),(0,2,2),(2,2,2) respectively. What is the angle between the diagonal of one of the faces of the cube

NDA 2010 Solution View →
Practice all Three Dimensional Geometry questions in the app →

Related NDA Mathematics chapters

Trigonometric Ratios & Identities (295)Statistics (236)Probability (201)Sequences and Series (182)Quadratic Equation (157)Matrices (153)Determinants (130)Functions (129)Permutation and Combination (129)Differential Equations (127)Definite Integration (110)Differentiation (104)

Three Dimensional Geometry in other exams

JEE Three Dimensional Geometry (756)BITSAT Three Dimensional Geometry (40)