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JEE Vector Algebra PYQs with Solutions

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

616 questionsMathematics2006–2026Answers + solutions

About Vector Algebra PYQs

Vector Algebra has 616 previous year questions in the Quantrex Academy JEE Main & Advanced Mathematics bank. The 220 questions in this list come from JEE Main (174) and JEE Advanced (46), 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: 25
  • 2025: 24
  • 2024: 35
  • 2023: 50
  • 2022: 30
  • 2021: 21
  • 2020: 2
  • 2019: 1
  • 2018: 2
  • 2017: 2
  • 2016: 1
  • 2015: 2

Vector Algebra questions with solutions

1

Let a , b be two vectors, and let P, Q and R be the points with position vectors a , b and a + b , respectively, with respect to the origin O . If | a + b | = 21 , | a - b | = 3

JEE Advanced 2026 Solution View → 2

Let a = 4 i - j + 3 k , b = 10 i + 2 j - k and a vector c be such that 2( a × b ) + 3( b × c ) = 0 . If a · c = 15 , then c ·( i + j -3 k ) is equal to:

JEE Main 2026 Solution View → 3

Let a = 2 i + 3 j + 3 k and b = 6 i + 3 j + 3 k . Then the square of the area of the triangle with adjacent sides determined by the vectors (2 a + 3 b ) and ( a - b ) is :

JEE Main 2026 Solution View → 4

If a = i + j + k , b = j - k and c be three vectors such that a × c = b and a · c = 3 , then c · ( a - 2 b ) is equal to _______.

JEE Main 2026 Solution View → 5

Let O be the origin, OP = a and OQ = b . If R is the point on OP such that OP = 5 OR , and M is the point such that OQ = 5 RM , then PM is equal to :

JEE Main 2026 Solution View → 6

Let a = 7 i + j - k and b = j + 2 k . If r is a vector such that r × a + a × b = 0 and r · a = 0 , then |3 r |^2 is equal to:

JEE Main 2026 Solution View → 7

Let u and v be unit vectors inclined at an acute angle such that | u × v |= 3 2 . If A =λ u + v +( u × v ) , then λ is equal to:

JEE Main 2026 Solution View → 8

Let a_k = ( θ_k) i + j and b_k = i - ( θ_k) j , where θ_k = 2^ k-1 π 2^n + 1 , for some n ∈ ℕ , n > 5 . Then the value of ∑_ k=1 ^ n | a_k |^2 ∑_ k=1 ^ n | b_k |^2 is _____.

JEE Main 2026 Solution View → 9

Let the vectors a = - i + j + 3 k and b = i + 3 j + k . For some λ, μ ∈ ℝ , let c = λ a + μ b . If c · (3 i - 6 j + 2 k ) = 10 and c · ( i + j + k ) = -2 , then | c |^2 is equal

JEE Main 2026 Solution View → 10

Two adjacent sides of a parallelogram PQRS are given by PQ = j + k and PS = i - j . If the side PS is rotated about the point P by an acute angle α in the plane of the

JEE Main 2026 Solution View → 11

If a and b are two vectors such that | a | = 2 and | b | = 3 , then the maximum value of 3|(3 a + 2 b )| + 4|(3 a - 2 b )| is :

JEE Main 2026 Solution View → 12

Let P be a point in the plane of the vectors A B =3 i + j - k and A C = i - j +3 k such that P is equidistant from the lines AB and AC. If | AP |= 5 2 , then the area of the

JEE Main 2026 Solution View → 13

For three unit vectors a , b , c satisfying | a - b |^ 2 +| b - c |^ 2 +| c - a |^ 2 =9 and |2 a +k b +k c |=3 , the positive value of k is

JEE Main 2026 Solution View → 14

Let P Q R be a triangle such that P Q =-2 i - j +2 k and PR =a i +b j -4 k , a, b ∈ ℤ . Let S be the point on QR, which is equidistant from the lines PQ and PR. If | PR |=9 and PS

JEE Main 2026 Solution View → 15

Let a =2 i -5 j +5 k and b = i - j +3 k . If c is a vector such that 2( a × c )+3( b × c )= 0 and ( a - b ) · c =-97 , then | c × k |^ 2 is equal to

JEE Main 2026 Solution View → 16

Let a =2 i - j - k , b = i +3 j - k and c =2 i + j +3 k . Let v be the vector in the plane of the vectors a and b , such that the length of its projection on the vector c is 1 14

JEE Main 2026 Solution View → 17

Let a =2 i + j -2 k , b = i + j and c = a × b . Let d be a vector such that | d - a |= 11 ,| c × d |=3 and the angle between c and d is (π)/(4) . Then a · d is equal to

JEE Main 2026 Solution View → 18

Let a = i -2 j +3 k , b =2 i + j - k , c =λ i + j + k and v = a × b . If v · c =11 and the length of the projection of b on c is p , then 9 p^ 2 is equal to

JEE Main 2026 Solution View → 19

Let a , b , c be three vectors such that a × b =2( a × c ) . If | a |=1,| b |=4,| c |=2 , and the angle between b and c is 60^ ∘ , then | a · c | is equal to

JEE Main 2026 Solution View → 20

Let a =- i + j +2 k , ~b = i - j -3 k , c = a × b and d = c × a . Then ( a - b ) · d is equal to :

JEE Main 2026 Solution View → 21

Let a =2 i - j + k and b =λ j +2 k , λ ∈ Z be two vectors. Let c = a × b and d be a vector of magnitude 2 in y z -plane. If | c |= 53 , then the maximum possible value of ( c · d

JEE Main 2026 Solution View → 22

Let a vector a = 2 i - j +λ k , λ>0 , make an obtuse angle with the vector b =-λ^ 2 i +4 2 j +4 2 k and an angle θ, (π)/(6)<θ<(π)/(2) , with the positive z -axis. If the set of

JEE Main 2026 Solution View → 23

Let AB =2 i +4 j -5 k and AD = i +2 j +λ k , λ ∈ ℝ . Let the projection of the vector v = i + j + k on the diagonal AC of the parallelogram ABCD be of length one unit. If α, β

JEE Main 2026 Solution View → 24

For a triangle ABC, let p = BC , q = CA and r = BA . If | p |=2 3 ,| q |=2 and θ= 1 3 , where θ is the angle between p and q , then | p ×( q -3 r )|^ 2 +3| r |^ 2 is equal to :

JEE Main 2026 Solution View → 25

Let a =- i +2 j +2 k , ~b =8 i +7 j -3 k and c be vector such that a × c = b . If c ·( i + j + k )=4 , then | a + c |^ 2 is equal to :

JEE Main 2026 Solution View → 26

For any two points M and N in the X Y -plane, let M N denote the vector from M to N , and 0 denote the zero vector. Let P, Q and R be three distinct points in the X Y -plane. Let

JEE Advanced 2025 Solution View → 27

Let w = i + j -2 k , and u and v be two vectors such that u × v = w and v × w = u . Let α, β, γ and t be real numbers such that u =α i +β j +γ k ,-t α+β+γ=0, α-t β+γ=0 , and α+β-t

JEE Advanced 2025 Solution View → 28

Consider the vectors x = i +2 j +3 k , y =2 i +3 j + k , and z =3 i + j +2 k For two distinct positive real numbers α and β , define X =α x +β y - z , Y =α y +β z - x , and Z =α z

JEE Advanced 2025 Solution View → 29

Let a = i +2 j + k and b =2 i + j - k . Let c be a unit vector in the plane of the vectors a and b and be perpendicular to a . Then such a vector c is :

JEE Main 2025 Solution View → 30

Let a and b be the vectors of the same magnitude such that | a + b |+| a - b | | a + b |-| a - b | = 2 +1 . Then | a + b |^2 | a |^2 is :

JEE Main 2025 Solution View → 31

Let the angle θ, 0 θ (π)/(2) between two unit vectors a and b be ^ -1 ( 65 9 ) . If the vector c =3 a +6 ~b +9( a × b ), then the value of 9( c · a )-3( c · b ) is

JEE Main 2025 Solution View → 32

Let the three sides of a triangle A B C be given by the vectors 2 i - j + k , i -3 j -5 k and 3 i -4 j -4 k . Let G be the centroid of the triangle A B C . Then 6(| AG |^2+| BG

JEE Main 2025 Solution View → 33

Consider two vectors u =3 i - j and v =2 i + j -λ k , λ 0 . The angle between them is given by ^ -1 ( 5 2 7 ) . Let v = v _1+ v _2 , where v _1 is parallel to u and v _2 is

JEE Main 2025 Solution View → 34

Let a = i +2 j + k , b =3 i -3 j +3 k , c =2 i - j +2 k and d be a vector such that b × d = c × d and a · d =4 . Then |( a × d )|^2 is equal to ______ .

JEE Main 2025 Solution View → 35

Let a = i + j + k , b =3 i +2 j - k , c =λ j +μ k and d be a unit vector such that a × d = b × d and c · d =1 , If c is perpendicular to a , then |3 λ d +μ c |^2 is equal to

JEE Main 2025 Solution View → 36

Let a =2 i -3 j +k, b =3 i +2 j +5 k and a vector c be such that ( a - c ) × b =-18 i -3 j +12 k and a · c =3 . If b × c = d , then | a · d | is equal to :

JEE Main 2025 Solution View → 37

Let A B C D be a tetrahedron such that the edges AB, AC and AD are mutually perpendicular. Let the areas of the triangles ABC, ACD and ADB be 5,6 and 7 square units respectively.

JEE Main 2025 Solution View → 38

If a is nonzero vector such that its projections on the vectors 2 i - j +2 k , i +2 j -2 k and k are equal, then a unit vector along a is:

JEE Main 2025 Solution View → 39

Let a be a unit vector perpendicular to the vectors b = i -2 j +3 k and c =2 i +3 j - k , and makes an angle of ^ -1 (-(1)/(3)) with the vector i + j + k . If a makes an angle of

JEE Main 2025 Solution View → 40

Let \( a = 2 i - j +3 k , ~b = 3 i -5 j + k \) and \( c \) be a vector such that \( a × c = c × b \) and \(( a + c ) ·( b + c )= 168\). Then the maximum value of \(| c |^2\) is :

JEE Main 2025 Solution View → 41

If the components of a =α i +β j +γ k along and perpendicular to b =3 i + j - k respectively, are (16)/(11)(3 i + j - k ) and (1)/(11)(-4 i -5 j -17 k ) , then α^2+β^2+γ^2 is

JEE Main 2025 Solution View → 42

Let A, B, C be three points in x y -plane, whose position vector are given by 3 i + j , i + 3 j and a i +(1-a) j respectively with respect to the origin O . If the distance of the

JEE Main 2025 Solution View → 43

Let a = i + j + k , b =2 i +2 j + k and d = a × b . If c is a vector such that a · c =| c | , | c -2 a |^2=8 and the angle between d and c is (π)/(4) , then |10-3 ~b · c |+| d × c

JEE Main 2025 Solution View → 44

Let the position vectors of three vertices of a triangle be 4 p + q -3 r ,-5 p + q +2 r and 2 p - q +2 r . If the position vectors of the orthocenter and the circumcenter of the

JEE Main 2025 Solution View → 45

Let a =3 i - j +2 k , ~b = a ×( i -2 k ) and c = b × k . Then the projection of c -2 j on a is :

JEE Main 2025 Solution View → 46

Let a = i +2 j +3 k , b =3 i + j - k and c be three vectors such that c is coplanar with a and b . If the vector C is perpendicular to b and a · c =5 , then | c | is equal to

JEE Main 2025 Solution View → 47

Let the position vectors of the vertices A, B and C of a tetrahedron A B C D be i +2 j + k , i +3 j -2 k and 2 i + j - k respectively. The altitude from the vertex D to the

JEE Main 2025 Solution View → 48

Let a and b be two unit vectors such that the angle between them is (π)/(3) . If λ a +2 b and 3 a -λ b are perpendicular to each other, then the number of values of λ in [-1,3] is

JEE Main 2025 Solution View → 49

Let c be the projection vector of b =λ i +4 k , λ 0 , on the vector a = i +2 j +2 k . If | a + c |=7 , then the area of the parallelogram formed by the vectors b and c is ________

JEE Main 2025 Solution View → 50

Let p =2 i + j +3 k and q = i - j + k . If for some real numbers α, β , and γ , we have 15 i +10 j +6 k =α(2 p + q )+β( p -2 q )+γ( p × q ) then the value of γ is

JEE Advanced 2024 Solution View → 51

Let O P =(α-1)/(α) i + j + k , O Q = i +(β-1)/(β) j + k and O R = i + j +(1)/(2) k be three vectors, where α, β ∈ ℝ-\ 0\ and O denotes the origin. If ( O P × O Q ) · O R =0 and

JEE Advanced 2024 Solution View → 52

Between the following two statements: Statement I : Let a = i +2 j -3 k and b =2 i + j - k . Then the vector r satisfying a × r = a × b and a · r =0 is of magnitude 10 . Statement

JEE Main 2024 Solution View → 53

Let a =2 i +α j + k , b =- i + k , c =β j - k , where α and β are integers and α β=-6 . Let the values of the ordered pair (α, β) , for which the area of the parallelogram of

JEE Main 2024 Solution View → 54

Let three vectors a =α i +4 j +2 k , b =5 i +3 j +4 k , c =x i +y j +z k form a triangle such that c = a - b and the area of the triangle is 5 6 . If α is a positive real number

JEE Main 2024 Solution View → 55

Let O A =2 a , O B =6 a +5 b and O C =3 b , where O is the origin. If the area of the parallelogram with adjacent sides OA and OC is 15 sq. units, then the area (in sq. units) of

JEE Main 2024 Solution View → 56

Let a =4 i - j + k , b =11 i - j + k and c be a vector such that ( a + b ) × c = c ×(-2 a +3 b ) . If (2 a +3 b ) · c =1670 , then | c |^2 is equal to :

JEE Main 2024 Solution View → 57

Let a = i +2 j +3 k , b =2 i +3 j -5 k and c =3 i - j +λ k be three vectors. Let r be anit vector along b + c . If r · a =3 , then 3 λ is equal to:

JEE Main 2024 Solution View → 58

The set of all α , for which the vectors a =α t i +6 j -3 k and b =t i -2 j -2 α t k are inclined at an obtuse angle for all t ∈ ℝ , is

JEE Main 2024 Solution View → 59

Let a =9 i -13 j +25 k , b =3 i +7 j -13 k and c =17 i -2 j + k be three given vectors. If r is a vector such that r × a =( b + c ) × a and r ·( b - c )=0 , then |593 r +67 a |^2

JEE Main 2024 Solution View → 60

Let a =2 i + j - k , b =(( a ×( i + j )) × i ) × i . Then the square of the projection of a on b is :

JEE Main 2024 Solution View → 61

Let a =6 i + j - k and b = i + j . If c is a is vector such that | c | ≥ 6, a · c =6| c |,| c - a |=2 2 and the angle between a × b and c is 60^ ∘ , then |( a × b ) × c | is equal

JEE Main 2024 Solution View → 62

Let a =2 i -3 j +4 k , b =3 i +4 j -5 k and a vector c be such that a ×( b + c )+ b × c = i +8 j +13 k . If a · c =13 , then (24- b · c ) is equal to_______

JEE Main 2024 Solution View → 63

Consider three vectors a , b , c . Let | a |=2,| b |=3 and a = b × c . If α ∈[0, (π)/(3)] is the angle between the vectors b and c , then the minimum value of 27| c - a |^2 is

JEE Main 2024 Solution View → 64

Let a =2 i +5 j - k , b =2 i -2 j +2 k and c be three vectors such that ( c + i ) ×( a + b + i )= a ×( c + i ) . If a · c =-29 , then c ·(-2 i + j + k ) is equal to:

JEE Main 2024 Solution View → 65

Let a = i -3 j +7 k , b =2 i - j + k and c be a vector such that ( a +2 b ) × c =3( c × a ) . If a · c =130 , then b · c is equal to _______

JEE Main 2024 Solution View → 66

Let a = i + j + k , b =2 i +4 j -5 k and c =x i +2 j +3 k , x ∈ ℝ . If d is the unit vector in the direction of b + c such that a · d =1 , then ( a × b ) · c is equal to

JEE Main 2024 Solution View → 67

For λ>0 , let θ be the angle between the vectors a = i +λ j -3 k and b =3 i - j +2 k . If the vectors a + b and a - b are mutually perpendicular, then the value of (14 cos θ)^2 is

JEE Main 2024 Solution View → 68

Let a unit vector which makes an angle of 60^ ∘ with 2 i +2 j - k and angle 45^ ∘ with i - k be C . Then C +(-(1)/(2) i + 1 3 2 j - 2 3 k ) is :

JEE Main 2024 Solution View → 69

Let ABC be a triangle of area 15 2 and the vectors AB = i +2 j -7 k , BC =a i +b j +ck and AC =6 i +d j -2 k , ~d>0 . Then the square of the length of the largest side of the

JEE Main 2024 Solution View → 70

Consider a where A(1, 3, 2), B(- 2, 8, 0) and C(3, 6, 7) . If the angle bisector of ∠ BAC meets the line BC at D , then the length of the projection of the vector → AD on the

JEE Main 2024 Solution View → 71

Let → a = ^ i + ^ j + ^ k , → b = - ^ i - 8 ^ j + 2 ^ k and → c = 4 ^ i + c _ 2 ^ j + c _ 3 ^ k be three vectors such that → b × → a = → c × → a . If the angle between the vector

JEE Main 2024 Solution View → 72

Let → a = - 5 ^ i + ^ j - 3 ^ k , → b = ^ i + 2 ^ j - 4 ^ k and → c = ((( → a × → b ) × ^ i ) × ^ i ) × ^ i . Then → c ⋅ (- ^ i + ^ j + ^ k ) is equal to

JEE Main 2024 Solution View → 73

Let → a = 3 ^ i + 2 ^ j + ^ k , → b = 2 ^ i - ^ j + 3 ^ k and → c be a vector such that ( → a + → b ) × → c = 2( → a × → b ) + 24 ^ j - 6 ^ k and ( → a - → b + ^ i ) . → c = - 3 .

JEE Main 2024 Solution View → 74

Let → a = 3 ^ i + ^ j - 2 ^ k , → b = 4 ^ i + ^ j + 7 ^ k and → c = ^ i - 3 ^ j + 4 ^ k be three vectors. If a vectors → p satisfies → p × → b = → c × → b and → p ⋅ → a = 0 , then

JEE Main 2024 Solution View → 75

Let → a and → b be two vectors such that | → a | = 1, | → b | = 4 and → a ⋅ → b = 2 . If → c = (2 → a × → b ) - 3 → b and the angle between → b and → c is α , then 192 ^ 2 α is

JEE Main 2024 Solution View → 76

Let → a = ^ i + α ^ j + β ^ k , α, β ∈ R . Let a vector → b be such that the angle between → a and → b is (π)/(4) and | → b | ^ 2 = 6 , If → a · → b = 3 2 , then the value of ( α

JEE Main 2024 Solution View → 77

Let → a and → b be two vectors such that | → b | = 1 and | → b × → a | = 2 Then | ( → b × → a ) - → b | ^ 2 is equal to

JEE Main 2024 Solution View → 78

Let A ( 2, 3, 5 ) and C ( - 3, 4, - 2 ) be opposite vertices of a parallelogram ABCD if the diagonal → BD = ^ i + 2 ^ j + 3 ^ k then the area of the parallelogram is equal to

JEE Main 2024 Solution View → 79

Let → a = a _ i ^ i + a _ 2 ^ j + a _ 3 ^ k and → b = b _ 1 ^ i + b _ 2 ^ j + b _ 3 ^ k be two vectors such that | → a | = 1; → a · → b = 2 and | → b | = 4 . If → c = 2 ( → a × →

JEE Main 2024 Solution View → 80

Let → OA = → a , → OB = 12 → a + 4 → b and → OC = → b , where O is the origin. If S is the parallelogram with adjacent sides OA and OC , then

JEE Main 2024 Solution View → 81

Let a unit vector ^ u = x ^ i + y ^ j + z ^ k make angles (π)/(2), (π)/(3) and (2π)/(3) with the vectors 1 2 ^ i + 1 2 ^ k , 1 2 ^ j + 1 2 ^ k and 1 2 ^ i + 1 2 ^ j respectively.

JEE Main 2024 Solution View → 82

Let → a , → b and → c be three non-zero vectors such that → b and → c are non-collinear if → a + 5 → b is collinear with → c , → b + 6 → c is collinear with → a and → a + α → b +

JEE Main 2024 Solution View → 83

If → a = ^ i + 2 ^ j + ^ k , → b = 3( ^ i - ^ j + ^ k ) and → c be the vector such that → a × → c = → b and → a · → c = 3 , then → a · ( ( → c × → b ) - → b - → c ) is equal to

JEE Main 2024 Solution View → 84

The least positive integral value of α , for which the angle between the vectors α ^ i - 2 ^ j + 2 ^ k and α ^ i + 2α ^ j - 2 ^ k is acute, is _____.

JEE Main 2024 Solution View → 85

Let the position vectors of points P, Q, R and S be → a = ^ i + 2 ^ j - 5 ^ k , → b = 3 ^ i + 6 ^ j + 3 ^ k , → c = (17)/(5) ^ i + (16)/(5) ^ j + 7 ^ k and → d = 2 ^ i + ^ j + ^ k

JEE Advanced 2023 Solution View → 86

Let P be the plane 3 x + 2y + 3z = 16 and let S = \ α ^ i + β ^ j + γ ^ k : α ^ 2 + β ^ 2 + γ ^ 2 = 1) and the distance of (α, β, γ) from the plane P is (7)/(2) . Let → u , → v

JEE Advanced 2023 Solution View → 87

Let S be the set of all (λ, μ) for which the vectors λ ^ i - ^ j + ^ k , ^ j + 2 ^ j + μ ^ k and 3 ^ i - 4 ^ j + 5 ^ k , where λ - μ = 5 , are coplanar, then ∑ _ (λ, μ) ∈ S 80 ( λ

JEE Main 2023 Solution View → 88

Let ABCD be a quadrilateral. If E and F are the mid points of the diagonals AC and BD respectively and ( → AB - → BC ) + ( → AD - → DC ) = k → FE , then k is equal to

JEE Main 2023 Solution View → 89

Let | → a | = 2, | → b | = 3 and the angle between the vectors → a and → b be (π)/(4) . Then | ( → a + 2 → b ) × ( 2 → a - 3 → b ) | ^ 2 is equal to

JEE Main 2023 Solution View → 90

Let for a triangle ABC → AB = - 2 ^ i + ^ j + 3 ^ k → CB = α ^ i + β ^ j + γ ^ k → CA = 4 ^ i + 3 ^ j + δ ^ k If δ > 0 and the area of the triangle ABC is 5 6 then → CB · → CA is

JEE Main 2023 Solution View → 91

Let → a = ^ i + 4 ^ j + 2 ^ k , → b = 3 ^ i - 2 ^ j + 7 ^ k and → c = 2 ^ i - ^ j + 4 ^ k . If a vector → d satisfies → d × → b = → c × → b and → d · → a = 24, then | → d | ^ 2 is

JEE Main 2023 Solution View → 92

Let → a = 3 ^ i + ^ j - ^ k and → c = 2 ^ i - 3 ^ j + 3 ^ k . If → b is a vector such that → a = → b × → c and | → b | ^ 2 = 50, then |72 - | → b + → c | ^ 2 | is equal to

JEE Main 2023 Solution View → 93

Let a, b, c be three distinct real numbers, none equal to one. If the vectors a ^ i + ^ j + ^ k , ^ i + b ^ j + ^ k and ^ i + ^ j + c ^ k are coplanar, then (1)/(1 - a) + (1)/(1

JEE Main 2023 Solution View → 94

Let λ ∈ ℤ, → a = λ ^ i + ^ j - ^ k and → b = 3 ^ i - ^ j + 2 ^ k . Let → c be a vector such that ( → a + → b + → c ) × → c = → 0 , → a · → c = - 17 and → b · → c = - 20 . Then | →

JEE Main 2023 Solution View → 95

Let the plane x + 3y - 2z + 6 = 0 meet the co-ordinate axes at the points A, B, C . If the orthocenter of the triangle ABC is (α, β, (6)/(7)) , then 98 (α + β) ^ 2 is equal to

JEE Main 2023 Solution View → 96

If four distinct points with position vectors → a , → b , → c and → d are coplanar, then [ → a → b → c ] is equal to

JEE Main 2023 Solution View → 97

Let → a = ^ i + 2 ^ j + 3 ^ k and → b = ^ i + ^ j - ^ k . If → c is a vector such that → a · → c = 11, → b · ( → a × → c ) = 27 and → b · → c = - 3 | → b | , then | → a × → c | ^

JEE Main 2023 Solution View → 98

For any vector → a = a _ 1 ^ i + a _ 2 ^ j + a _ 3 ^ k , with 10| a _ i | (A) : max\ | a _ 1 |, | a _ 2 |, | a _ 3 |\ ≤ | → a | (B) : | → a | ≤ 3max\ | a _ 1 |, | a _ 2 |, | a _ 3

JEE Main 2023 Solution View → 99

Let → a be a non-zero vector parallel to the line of intersection of the two planes described by ^ i + ^ j , ^ i + ^ k and ^ i - ^ j , ^ j - ^ k . If θ is the angle between the

JEE Main 2023 Solution View → 100

Let → a = 2 ^ i + 7 ^ j - ^ k , ^ b = 3 ^ i + 5 ^ k and → c = ^ i - ^ j + 2 ^ k Let → d be a vector which is perpendicular to both → a and → b , and → c · → d = 12 . Then (- ^ i +

JEE Main 2023 Solution View → 101

If the points P and Q are respectively the circumcenter and the orthocentre of a ∆ ABC , then → PA + → PB + → PC is equal to _______

JEE Main 2023 Solution View → 102

An arc PQ of a circle subtends a right angle at its centre O . The mid point of the arc PQ is R . If → OP = → u , → OR = → v and → OQ = α → u + β → v , then α, β ^ 2 , are the

JEE Main 2023 Solution View → 103

Let O be the origin and the position vector of the point P be - ^ i - 2 ^ j + 3k . If the position vectors of the points A, B and C are - 2 ^ i + ^ j - 3k, 2 ^ i + 4 ^ j - 2k and

JEE Main 2023 Solution View → 104

Let the vectors → u _ 1 = ^ i + ^ j + a ^ k , → u _ 2 = ^ i + b ^ j + ^ k , and → u _ 3 = c ^ i + ^ j + ^ k be coplanar. If the vectors → v _ 1 = (a + b) ^ i + c ^ j + c ^ k , → v

JEE Main 2023 Solution View → 105

The area of the quadrilateral ABCD with vertices A ( 2, 1, 1 ) , B ( 1, 2, 5 ) , C ( - 2, - 3, 5 ) and D ( 1, - 6, - 7 ) is equal to

JEE Main 2023 Solution View → 106

If the points with position vectors α ^ i + 10 ^ j + 13 ^ k , 6 ^ i + 11 ^ j + 11 ^ k , (9)/(2) ^ i + β ^ j - 8 ^ k are collinear, then (19α - 6β) ^ 2 is equal to

JEE Main 2023 Solution View → 107

Let → a = 6 ^ i + 9 ^ j + 12 ^ k , → b = α ^ i + 11 ^ j - 2 ^ k and → c be vectors such that → a × → c = → a × → b If → a · → c = - 12, and → c · ( ^ i - 2 ^ j + ^ k ) = 5 then →

JEE Main 2023 Solution View → 108

Let the vectors → a , → b , → c represent three coterminous edges of a parallelopiped of volume V . Then the volume of the parallelopiped, whose coterminous edges are represented

JEE Main 2023 Solution View → 109

The sum of all values of α , for which the points whose position vectors are ^ i - 2 ^ j + 3 ^ k , 2 ^ i - 3 ^ j + 4 ^ k , (α + 1) ^ i + 2 ^ k and 9 ^ i + (α - 8) ^ j + 6 ^ k are

JEE Main 2023 Solution View → 110

Let the position vectors of the points A, B, C and D be 5 ^ i + 5 ^ j + 2λ ^ k , ^ i + 2 ^ j + 3 ^ k , - 2 ^ i + λ ^ j + 4 ^ k and - ^ i + 5 ^ j + 6 ^ k . Let the set S = λ ∈ ℝ

JEE Main 2023 Solution View → 111

Let → a = 2 ^ i + 3 ^ j + 4 ^ k , → b = ^ i - 2 ^ j - 2 ^ k and → c = - ^ i + 4 ^ j + 3 ^ k . If → d is a vector perpendicular to both → b and → c , and → a · → d = 18, then | → a

JEE Main 2023 Solution View → 112

Let → a = 5 ^ i - ^ j - 3 ^ k and → b = ^ i + 3 ^ j + 5 ^ k be two vectors. Then which one of the following statements is TRUE?

JEE Main 2023 Solution View → 113

Let → a = 2 ^ i - 7 ^ j + 5 ^ k , → b = ^ i + ^ k and → c = ^ i + 2 ^ j - 3 ^ k be three given vectors. If → r is a vector such that → r × → a = → c × → a and → r · → b = 0 , then

JEE Main 2023 Solution View → 114

Let → v = α ^ i + 2 ^ j - 3 ^ k , → w = 2α ^ i + ^ j - ^ k , and → u be a vector such that | → u | = α > 0 . If the minimum value of the scalar triple product [ → u → v → w ] is

JEE Main 2023 Solution View → 115

A(2, 6, 2), B(- 4, 0, λ), C(2, 3, - 1) and D(4, 5, 0), |λ| ≤ 5 are the vertices of a quadrilateral ABCD . If its area is 18 square units, then 5 - 6λ is equal to _____ .

JEE Main 2023 Solution View → 116

Let → a = ^ i + 2 ^ j + 3 ^ k , → b = ^ i - ^ j + 2 ^ k and → c = 5 ^ i - 3 ^ j + 3 ^ k , be there(three) vector. If → r is a vector such that, → r × → b = → c × → b and → r · → a

JEE Main 2023 Solution View → 117

Let → a , → b , → c be three vectors such that | → a | = 31 , 4| → b | = | → c | = 2 and 2( → a × → b ) = 3( → c × → a ) . If the angle between → b and → c is (2π)/(3) , then ( →

JEE Main 2023 Solution View → 118

Let → a = 2 ^ i + ^ j + ^ k , and → b and → c be two nonzero vectors such that | → a + → b + → c | = | → a + → b - → c | and → b · → c = 0. Consider the following two statement

JEE Main 2023 Solution View → 119

Let → a and → b be two vector such that | → a | = 14 , | → b | = 6 and | → a × → b | = 48 . Then ( → a · → b ) ^ 2 is equal to _____ .

JEE Main 2023 Solution View → 120

Let λ ∈ ℝ, → a = λ ^ i + 2 ^ j - 3 ^ k , → b = ^ i - λ ^ j + 2 ^ k , If ( ( → a + → b ) × ( → a × → b ) ) × ( → a - → b ) = 8 ^ i - 40 ^ j - 24 ^ k then | λ ( → a + → b ) × ( → a

JEE Main 2023 Solution View → 121

Let → a and → b be two vectors. Let | → a | = 1, | → b | = 4 and → a · → b = 2 . If → c = ( 2 → a × → b ) - 3 → b , then the value of → b · → c is

JEE Main 2023 Solution View → 122

If → a , → b , → c are three non-zero vectors and ^ n is a unit vector perpendicular to → c such that → a = α → b - ^ n , (α ≠ 0) and → b · → c = 12 , then | → c × ( → a × → b )|

JEE Main 2023 Solution View → 123

If → a = ^ i + 2 ^ k , → b = ^ i + ^ j + ^ k , → c = 7 ^ i - 3 ^ j + 4 ^ k , → r × → b + → b × → c = → 0 and → r · → a = 0 then → r . → c is equal to:

JEE Main 2023 Solution View → 124

Let → a = 4 ^ i + 3 ^ j and → b = 3 ^ i - 4 ^ j + 5 ^ k and → c is a vector such that → c · ( → a × → b ) + 25 = 0, → c · ( ^ i + ^ j + ^ k ) = 4 and projection of → c on → a is 1

JEE Main 2023 Solution View → 125

If the vectors → a = λ ^ i + μ ^ j + 4 ^ k , → b = - 2 ^ i + 4 ^ j - 2 ^ k and → c = 2 ^ i + 3 ^ j + ^ k are coplanar and the projection of → a on the vector → b is 54 units, then

JEE Main 2023 Solution View → 126

Let → a , → b and → c be three non-zero non-coplanar vectors. Let the position vectors of four points A, B, C and D be → a - → b + → c , λ → a - 3 → b + 4 → c , - → a + 2 → b - 3

JEE Main 2023 Solution View → 127

If the four points, whose position vectors are 3 ^ i - 4 ^ j + 2 ^ k , ^ i + 2 ^ j - ^ k , - 2 ^ i - ^ j + 3 ^ k and 5 ^ i - 2α ^ j + 4 ^ k are coplanar, then α is equal to

JEE Main 2023 Solution View → 128

Let → a = - ^ i - ^ j + ^ k , → a · → b = 1 and → a × → b = ^ i - ^ j . Then → a - 6 → b is equal to

JEE Main 2023 Solution View → 129

Let → a , → b and → c be three non zero vectors such that → b · → c = 0 and → a × ( → b × → c ) = → b - → c 2 . If → d be a vector such that → b · → d = → a · → b , then ( → a × →

JEE Main 2023 Solution View → 130

The vector → a = - ^ i + 2 ^ j + ^ k is rotated through a right angle, passing through the y -axis in its way and the resulting vector is → b . Then the projection of 3 → a + 2 →

JEE Main 2023 Solution View → 131

Let → α = 4 ^ i + 3 ^ j + 5 ^ k and → β = ^ i + 2 ^ j - 4 ^ k . Let → β 1 be parallel to → α and → β 2 be perpendicular to → α . If → β = → β 1 + → β 2 , then the value of 5 → β 2

JEE Main 2023 Solution View → 132

Let → a = ^ i + 2 ^ j + λ ^ k , → b = 3 ^ i - 5 ^ j - λ ^ k , → a · → c = 7 , 2( → b · → c ) + 43 = 0 , → a × → c = → b × → c , then → a · → b is equal to

JEE Main 2023 Solution View → 133

Let → u = ^ i - ^ j - 2 ^ k , → v = 2 ^ i + ^ j - ^ k , → v · → w = 2 and → v × → w = → u + λ → v , then → u · → w is equal to

JEE Main 2023 Solution View → 134

Let PQR be a triangle. The points A, B and C are on the sides QR, RP and PQ respectively such that (QA)/(AR) = (RB)/(BP) = (PC)/(CQ) = (1)/(2) . Then (Area(∆ PQR))/(Area(∆ ABC))

JEE Main 2023 Solution View → 135

Let ^ i , ^ j and ^ k be the unit vectors along the three positive coordinate axes. Let → a = 3 ^ i + ^ j - ^ k → b = ^ i + b _ 2 ^ j + b _ 3 ^ k , b _ 2 , b _ 3 ∈ ℝ → c = c _ 1 ^

JEE Advanced 2022 Solution View → 136

If (2, 3, 9), (5, 2, 1), (1, λ, 8) and (λ, 2, 3) are coplanar, then the product of all possible values of λ is

JEE Main 2022 Solution View → 137

Let → a , → b , → c be three coplanar concurrent vectors such that angles between any two of them is same. If the product of their magnitudes is 14 and ( → a × → b ) · ( → b × → c

JEE Main 2022 Solution View → 138

Let → a and → b be two vectors such that | → a + → b | ^ 2 = | → a | ^ 2 + 2 | → b | ^ 2 , → a · → b = 3 and | → a × → b | ^ 2 = 75 . Then | → a | ^ 2 is equal to ______.

JEE Main 2022 Solution View → 139

Let → a = 3 ^ i + ^ j and → b = ^ i + 2 ^ j + ^ k . Let → c be a vector satisfying → a × ( → b × → c ) = → b + λ → c . If → b and → c are non-parallel, then the value of λ is

JEE Main 2022 Solution View → 140

Let ^ a and ^ b be two unit vectors such that the angle between them is (π)/(4) . If θ is the angle between the vectors ( ^ a + ^ b ) and ( ^ a + 2 ^ b + 2( ^ a × ^ b )) then the

JEE Main 2022 Solution View → 141

Let S be the set of all a ∈ R for which the angle between the vectors → u = a( _ e b) ^ i - 6 ^ j + 3 ^ k and → v = ( _ e b) ^ i + 2 ^ j + 2a( _ e b) ^ k , (b > 1) is acute. Then

JEE Main 2022 Solution View → 142

Let the vectors → a = (1 + t) ^ i + (1 - t) ^ j + ^ k , → b = (1 - t) ^ i + (1 + t) ^ j + 2 ^ k and → c = t ^ i - t ^ j + ^ k , t ∈ R be such that for α, β, γ ∈ R, α → a + β → b +

JEE Main 2022 Solution View → 143

Let a vector → a has a magnitude 9 . Let a vector → b be such that for every (x, y)R × R - \ (0, 0)\ , the vector (x → a + y → b ) is perpendicular to the vector (6y → a - 18x → b

JEE Main 2022 Solution View → 144

Let → a , → b , → c be three non-coplanar vectors such that → a × → b = 4 → c , → b × → c = 9 → a and → c × → a = α → b , α > 0 If | → a | + | → b | + | → c | = 36 , then α is

JEE Main 2022 Solution View → 145

Let → a = α ^ i + ^ j + β ^ k and → b = 3 ^ i - 5 ^ j + 4 ^ k be two vectors, such that → a × → b = - ^ i + 9 ^ i + 12 ^ k . Then the projection of → b - 2 → a on → b + → a is

JEE Main 2022 Solution View → 146

Let → a = 2 ^ i - ^ j + 5 ^ k and → b = α ^ i + β ^ j + 2 ^ k . If (( → a × → b ) × ^ i ) · ^ k = (23)/(2) , then | → b × 2 ^ j | is equal to

JEE Main 2022 Solution View → 147

Let → a = α ^ i + ^ j - ^ k and → b = 2 ^ i + ^ j - α ^ k , α > 0 . If the projection of → a × → b on the vector - ^ i + 2 ^ j - 2 ^ k is 30 , then α is equal to

JEE Main 2022 Solution View → 148

Let → a = ^ i - ^ j + 2 ^ k and let → b be a vector such that → a × → b = 2 ^ i - ^ k and → a · → b = 3 . Then the projection of → b on the vector → a - → b is:

JEE Main 2022 Solution View → 149

Let ABC be a triangle such that → BC = → a , → CA = → b , → AB = → c , | → a | = 6 2 , | → b | = 2 3 and → b · → c = 12 Consider the statements : (S1) : |( → a × → b ) + ( → c × →

JEE Main 2022 Solution View → 150

Let A, B, C be three points whose position vectors respectively are: → a = ^ i + 4 ^ j + 3 ^ k → b = 2 ^ i + α ^ j + 4 ^ k , α ∈ R → c = 3 ^ i - 2 ^ j + 5 ^ k If α is the smallest

JEE Main 2022 Solution View → 151

Let → a = ^ i - 2 ^ j + 3 ^ k , → b = ^ i + ^ j + ^ k and → c be a vector such that → a × ( → b + → c ) = → 0 , then the value of 3( → c . → a ) is equal to _______.

JEE Main 2022 Solution View → 152

Let → a = α ^ i + 3 ^ j - ^ k , → b = 3 ^ i - β ^ j + 4 ^ k and → c = ^ i + 2 ^ j - 2 ^ k where α, β ∈ R be three vectors. If the projection of → a on → c is (10)/(3) and → b × →

JEE Main 2022 Solution View → 153

Let → a = α ^ i + 2 ^ j - ^ k and → b = - 2 ^ i + α ^ j + ^ k , where α ∈ R . If the area of the parallelogram whose adjacent sides are represented by the vectors → a and → b is

JEE Main 2022 Solution View → 154

Let → a be a vector which is perpendicular to the vector 3 ^ i + (1)/(2) ^ j + 2 ^ k . If → a × (2 ^ i + ^ k ) = 2 ^ i - 13 ^ j - 4 ^ k , then the projection of the vector → a on

JEE Main 2022 Solution View → 155

If → a = 2 ^ i + ^ j + 3 ^ k , → b = 3 ^ i + 3 ^ j + ^ k and → c = c _ 1 ^ i + c _ 2 ^ j + c _ 3 ^ k are coplanar vectors and → a · → c = 5, → b ⊥ → c , then 122( c _ 1 + c _ 2 +

JEE Main 2022 Solution View → 156

Let → a and → b be the vectors along the diagonal of a parallelogram having area 2 2 . Let the angle between → a and → b be acute. | → a | = 1 and | → a . → b | =| → a × → b |. If

JEE Main 2022 Solution View → 157

Let → a = ^ i + ^ j - ^ k and → c = 2 ^ i - 3 ^ j + 2 ^ k . Then the number of vectors → b such that → b × → c = → a and | → b | ∈\ 1, 2, … , 10\ is

JEE Main 2022 Solution View → 158

Let → a = ^ i + ^ j + 2 ^ k , → b = 2 ^ i - 3 ^ j + ^ k and → c = ^ i - ^ j + ^ k be the three given vectors. Let → v be a vector in the plane of → a and → b whose projection on →

JEE Main 2022 Solution View → 159

If → a · → b = 1, → b · → c = 2 and → c · → a = 3 , then the value of [ → a × ( → b × → c ) → b × ( → c × → a ) → c × ( → b × → a ) ] is

JEE Main 2022 Solution View → 160

Let → b = ^ i + ^ j + λ ^ k , λ ∈ ℝ . If → a is a vector such that → a × → b = 13 ^ i - ^ j - 4 ^ k and → a · → b + 21 = 0 , then ( → b - → a ) · ( ^ k - ^ j ) + ( → b + → a ) · (

JEE Main 2022 Solution View → 161

Let → a = a _ 1 ^ i + a _ 2 ^ j + a _ 3 ^ k , a _ i > 0, i = 1, 2, 3 be a vector which makes equal angles with the coordinate axes OX, OY and OZ . Also, let the projection of → a

JEE Main 2022 Solution View → 162

Let θ be the angle between the vectors → a and → b , where | → a | = 4, | → b | = 3 and θ ∈ ((π)/(4), (π)/(3)) . Then |( → a - → b ) × ( → a + → b )| ^ 2 + 4 ( → a · → b ) ^ 2 is

JEE Main 2022 Solution View → 163

Let a and b be two unit vectors such that |(a + b) + 2(a × b)| = 2 . If θ ∈ (0, π) is the angle between ^ a and ^ b , then among the statements: (S1): 2| ^ a × ^ b | = | ^ a - ^ b

JEE Main 2022 Solution View → 164

Let ^ a , ^ b be unit vectors. If → c be a vector such that the angle between ^ a and → c is (π)/(12) , and ^ b = → c + 2( → c × ^ a ) , then |6 → c | ^ 2 is equal to:

JEE Main 2022 Solution View → 165

Let O be the origin and → OA = 2 ^ i + 2 ^ j + ^ k , → OB = ^ i - 2 ^ j + 2 ^ k and → OC = (1)/(2)( → OB - λ → OA ) for some λ > 0 . If | → OB × → OC | = (9)/(2) , then which of

JEE Advanced 2021 Solution View → 166

Let → u , → v and → w be vectors in three-dimensional space, where → u and → v are unit vectors which are not perpendicular to each other and → u · → w = 1, → v · → w = 1, → w · →

JEE Advanced 2021 Solution View → 167

Let → a = 2 ^ i - ^ j + 2 ^ k and → b = ^ i + 2 ^ j - ^ k . Let a vector → v be in the plane containing → a and → b . If → v is perpendicular to the vector 3 ^ i + 2 ^ j - ^ k and

JEE Main 2021 Solution View → 168

Let → a , → b , → c be three vectors mutually perpendicular to each other and have same magnitude. If a vector → r satisfies → a × ( → r - → b ) × → a + → b × ( → r - → c ) × → b

JEE Main 2021 Solution View → 169

Let → a and → b be two vectors such that | 2 → a + 3 → b | = | 3 → a + → b | and the angle between → a and → b is 60 ° . If (1)/(8) → a is a unit vector, then | → b | is equal to :

JEE Main 2021 Solution View → 170

Let → a = ^ i + 5 ^ j + α ^ k , → b = ^ i + 3 ^ j + β ^ k and → c = - ^ i + 2 ^ j - 3 ^ k be three vectors such that, | → b × → c | = 5 3 and → a is perpendicular to → b . Then

JEE Main 2021 Solution View → 171

A hall has a square floor of dimension 10m × 10m (see the figure) and vertical walls. If the angle GPH between the diagonals AG and BH is ^ - 1 (1)/(5), then the height of the

JEE Main 2021 Solution View → 172

If the projection of the vector ^ i + 2 ^ j + ^ k on the sum of the two vectors 2 ^ i + 4 ^ j - 5 ^ k and - λ ^ i + 2 ^ j + 3 ^ k is 1 , then λ is equal to _______.

JEE Main 2021 Solution View → 173

Let → a = ^ i + ^ j + ^ k and → b = ^ j - ^ k . If → c is a vector such that → a × → c = → b and → a · → c = 3 , then → a · ( → b × → c ) is equal to:

JEE Main 2021 Solution View → 174

Let → a , → b and → c be three vectors such that → a = → b × ( → b × → c ) . If magnitudes of the vectors → a , → b and → c are 2 , 1 and 2 respectively and the angle between → b

JEE Main 2021 Solution View → 175

Let → a = ^ i - α ^ j + β ^ k , → b = 3 ^ i + β ^ j - α ^ k and → c = - α ^ i - 2 ^ j + ^ k , where α and β are integers. If → a · → b = - 1 and → b · → c = 10, then ( → a × → b )

JEE Main 2021 Solution View → 176

Let → a = ^ i + ^ j + 2 ^ k and → b = - ^ i + 2 ^ j + 3 ^ k . Then the vector product ( → a + → b ) × (( → a × (( → a - → b ) × → b )) × → b ) is equal to :

JEE Main 2021 Solution View → 177

Let → a = ^ i + ^ j + ^ k , → b and → c = ^ j - ^ k be three vectors such that → a × → b = → c and → a · → b = 1 . If the length of projection vector of the vector → b on the

JEE Main 2021 Solution View → 178

Let a, b and c be distinct positive numbers. If the vectors a ^ i + a ^ j + c ^ k , ^ i + ^ k and c ^ i + c ^ j + b ^ k are co-planar, then c is equal to:

JEE Main 2021 Solution View → 179

If | → a | = 2, | → b | = 5 and | → a × → b | = 8, then | → a · → b | is equal to:

JEE Main 2021 Solution View → 180

If → a and → b are unit vectors and ( → a + 3 → b ) is perpendicular to (7 → a - 5 → b ) and ( → a - 4 → b ) is perpendicular to (7 → a - 2 → b ), then the angle between → a and →

JEE Main 2021 Solution View → 181

Let the vectors (2 + a + b) ^ i + (a + 2b + c) ^ j - (b + c) ^ k , (1 + b) ^ i + 2b ^ j - b ^ k and (2 + b) ^ i + 2b ^ j + (1 - b) ^ k , ∀ a, b, c ∈ R be co-planar. Then which of

JEE Main 2021 Solution View → 182

Let → p = 2 ^ i + 3 ^ j + ^ k and → q = ^ i + 2 ^ j + ^ k be two vectors. If a vector → r = (α ^ i + β ^ j + γ ^ k ) is perpendicular to each of the vectors ( → p + → q ) and ( →

JEE Main 2021 Solution View → 183

Let a vector → a be coplanar with vectors → b = 2 ^ i + ^ j + ^ k and → c = ^ i - ^ j + ^ k . If → a is perpendicular to → d = 3 ^ i + 2 ^ j + 6 ^ k , and | → a | = 10 . Then a

JEE Main 2021 Solution View → 184

Let three vectors → a , → b and → c be such that → a × → b = → c , → b × → c = → a and | → a | = 2 . Then which one of the following is not true?

JEE Main 2021 Solution View → 185

In a triangle ABC, if | → BC | = 3, | → CA | = 5 and | → BA | = 7, then the projection of the vector → BA on → BC is equal to

JEE Main 2021 Solution View → 186

Let a and b be positive real numbers. Suppose → PQ = a ^ i + b ^ j and → PS = a ^ i - b ^ j are adjacent sides of a parallelogram PQRS . Let → u and → v be the projection vectors

JEE Advanced 2020 Solution View → 187

In a triangle PQR , let → a = → QR , → b = → RP and → c = → PQ . If | → a | = 3, | → b | = 4 and → a . ( → c - → b ) → c . ( → a - → b ) = | → a | | → a | + | → b | , then the

JEE Advanced 2020 Solution View → 188

Let → a = 2 ^ i + ^ j - ^ k and → b = ^ i + 2 ^ j + ^ k be two vectors. Consider a vector → c = α → a + β → b , α, β ∈ R . If the projection of → c on the vector ( → a + → b ) is

JEE Advanced 2019 Solution View → 189

Consider the cube in the first octant with sides OP, OQ and OR of length 1 , along the x-axis, y-axis and z-axis, respectively, where O ( 0, 0, 0 ) is the origin. Let S((1)/(2)

JEE Advanced 2018 Solution View → 190

Let → a and → b be two unit vectors such that → a . → b = 0 . For some x, y ∈ R, let → c = x → a + y → b + ( → a × → b ) . If | → c | = 2 and the vector → c is inclined at the

JEE Advanced 2018 Solution View → 191

Let O be the origin and let PQR be an arbitrary triangle. The point S is such that → OP . → OQ + → OR . → OS = → OR . → OP + → OQ . → OS = → OQ . → OR + → OP . → OS then triangle

JEE Advanced 2017 Solution View → 192

Paragraph: Let O be the origin, and O X , O Y , O Z be three unit vectors in the directions of the sides Q R , R P , P Q , respectively, of a triangle P Q R . Question: | O X × O

JEE Advanced 2017 Solution View → 193

Let ^ u = u _ 1 ^ i + u _ 2 ^ j + u _ 3 ^ k be a unit vector in ℝ ^ 3 and ^ w = 1 6 ( ^ i + ^ j + 2 ^ k ) . Given that there exists a vector → v in ℝ ^ 3 such that | ^ u × → v | =

JEE Advanced 2016 Solution View → 194

Suppose that → p , → q and → r are three non - coplanar vectors in ℝ ^ 3 . Let the components of a vector → s along \(p, q\) and \(r\) be 4,3 and 5 respectively. If the components

JEE Advanced 2015 Solution View → 195

Let be a triangle. Let → a = → QR , → b = → RP and → c = → PQ . If | → a | = 12, | → b | = 4 3 and → b ⋅ → c = 24, then which of the following is (are) true ?

JEE Advanced 2015 Solution View → 196

Let → x , → y and → z be three vectors each of magnitude 2 and the angle between each pair of them is (π)/(3) . If → a is a non - zero vector perpendicular to → x and → y × → z

JEE Advanced 2014 Solution View → 197

Let → a , → b and → c be three non - coplanar unit vectors such that the angle between every pair of them is (π)/(3) . If → a × → b + → b × → c = p → a + q → b + r → c , where p

JEE Advanced 2014 Solution View → 198

Match List-I with List - II and select the correct answer using the code given below the lists& & & List-I & List-II A. Volume of parallelepiped determined by vectors & &#8594; a

JEE Advanced 2013 Solution View → 199

Let → PR = 3 ^ i ⁡ + ^ j ⁡ - 2 ^ k and → SQ = ^ i ⁡ - 3 ^ j ⁡ - 4 ^ k determine diagonals of a parallelogram PQRS and → PT = ^ i ⁡ + 2 ^ j ⁡ + 3 ^ k be another vector. Then the

JEE Advanced 2013 Solution View → 200

Consider the set of eight vectors V = \ a ^ i + b ^ j + c ^ k : a, b, c ∈ \ - 1 , 1\ \ . Three non-coplanar vectors can be chosen fro m V in 2 ^ p ways. Then p is

JEE Advanced 2013 Solution View →
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Related JEE Mathematics chapters

Application of Derivatives (795)Three Dimensional Geometry (756)Sequences and Series (748)Functions (700)Definite Integration (692)Differential Equations (586)Continuity and Differentiability (576)Probability (561)Complex Number (551)Binomial Theorem (550)Quadratic Equation (517)Determinants (508)

Vector Algebra in other exams

NDA Vector Algebra (100)BITSAT Vector Algebra (25)