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# JEE Main Math Vectors Questions Answer Keys Solutions

Welcome to AMBiPi (Read as: एम्बीपाई) (Amans Maths Blogs). JEE Mains and JEE Advanced exams are the engineering entrance exams for taking admission in IITs, NITs and other engineering colleges. In this article, you will get JEE Main Math Vectors Questions Answer Keys Solutions.

### JEE Mains Mathematics Vectors Questions Bank

JEE Vector Questions No:91

Let α = (λ – 2) a + b and β = (4λ – 2) a + 3b be two given vectors where vectors a and b are non-collinear. The value of λ for which vectors α and β are collinear, is

[2019]

Option A: -4

Option B: -3

Option C: 4

Option D: 3

Option A: -4

JEE Main Vector Questions No: 92

Let √3i + j, i + √3j and βi + (1 – β)j respectively be the position vectors of the points A, B and C with respect to the origin O. If the distance of C from the bisector of the acute angle between OA and OB is 3 / √2 then the sum of all possible values of β is :

[2019]

Option A: 4

Option B: 3

Option C: 2

Option D: 1

Option D: 1

JEE Mathematics Vector Questions No: 93

Let a = i + 2j + 4k, b = i + ????j + 4k and c = 2î + 4j + (????² − 1)k be coplanar vectors. Then the non-zero vector a × c is

[2019]

Option A: -10i – 5j

Option B: -14i – 5j

Option C-14i + 5j

Option D: -10i + 5j

Option D: -10i + 5j

JEE Mathematics Vector Questions No: 94

The sum of the distinct real values of μ, for which the vectors, µi + j + k, i + µj + k, i + j + µk, are co-planar is

[2019]

Option A: -1

Option B: 0

Option C: 1

Option D: 2

Option A: -1

Vector JEE Questions No: 95

If a unit vector a makes angles π/3 with i, (n/4) with j and θ ∈ (0, π) with k, then a value of θ, is:

[2019]

Option A: (5π / 6)

Option B: (π / 4)

Option C: (5π / 12)

Option D: (2π / 3)

Option D: (2π / 3)

Vector JEE Main Questions No: 96

Let α ∈ R and the three vectors a = αi + j + 3k, b = 2i + j – αk and c = αî – 2j + 3k. Then the set S = (α: a, b and c are coplanar)

[2019]

Option A: is singleton

Option B: is empty

Option C: contains exactly two positive numbers

Option D: contains exactly two numbers only one of which is positive

Option B: is empty

JEE Main Math Vector Questions No: 97

If the volume of parallelopiped formed by the vectors i + λj + k, j + λk and λi + k is minimum, then λ is equal to:

[2019]

Option A: (-1 / √3)

Option B: (1 / √3)

Option C: √3

Option D: -√3

Option B: (1 / √3)

JEE Main Math Vector Questions No: 98

Let a = 3i + 2j + 2k and b = i + 2j – 2k be two vectors. If a vector perpendicular to both the vectors a + b and a b has the magnitude 12 then one such vector is

[2019]

Option A: 4(2i + 2j + 2k)

Option B: 4(2i – 2j k)

Option C: 4(2i + 2j k)

Option D: 4(-2i – 2j + k)

Option B: 4(2i – 2j – k)

JEE Main Vector Questions No: 99

Let a = i – 2j + k and b = i j + k be two vectors. If c is a vector such that b × c = b × a and c ∙ a = 0, then c ∙ b is equal to:

[2020]

Option A: (-3 / 2)

Option B: (1 / 2)

Option C: (-1 / 2)

Option D: -1

Option C: (-1 / 2)

JEE Mathematics Vector Questions No: 100

Let ab and c be three vectors such that | a | = √3, | b | = 5, b ∙ c = 10 and the angle between b and c is (π/3). If b is perpendicular to the vector b × c  then | a × (b × c) is equal to

[2020]

Correct Ans: 30

JEE Main Math Vector Questions No: 101

If a = 2i + 3j + 2k, then the value of | i × (a × i) |² + | j × (a × j) |² + | k × (a × k) |² is equal to

[2020]

Correct Ans: 18

Vector JEE Questions No: 102

Let x0, be the point of local maxima of f(x) = a ∙ (b × c), where a = xi – 2j + 3k, b = -2i + xj k and c = 7î – 2j + xk. Then the value of a ∙ b + b ∙ c + c ∙ a at x = x0 is:

[2020]

Option A: -4

Option B: -30

Option C: 14

Option D: -22

Option D: -22

Vector JEE Main Questions No: 103

If the volume of a parallelepiped, whose coterminous edges are given by the vectors a = i + j + nk, b = 2i + 4j – nk and c = i + nj + 3k (n ≥ 0), is 158 cu. units, then:

[2020]

Option A: a ∙ c = 17

Option B: b ∙ c = 10

Option C: n = 7

Option D: n = 9

Option B: b ∙ c = 10

JEE Mathematics Vector Questions No: 104

A vector a = αi + 2j + βk (α, β ∈ R) lies in the plane of the vectors, b = i + j and c = i j + 4k. If a bisects the angle between b and c, then:

[2020]

Option A: a i + 3 = 0

Option B: a i + 1 = 0

Option C: a k + 2 = 0

Option D: a k + 4 = 0

Option C: a ∙ k + 2 = 0

Vector JEE Questions No: 105

Let the volume of a parallelepiped whose coterminous edges are given by u = i + j + ????k, v = i + j + 3k and w = 2i + j + k be 1 cu. unit. If θ be the angle between the edges ū and w, then cosθ can be:

[2020]

Option A: (7 / 6√6)

Option B: (7 / 6√3)

Option C: (5 / 7)

Option D: (5 / 3√3)

Option B: (7 / 6√3)

Vector JEE Main Questions No: 106

The projection of the line segment joining the points (1, -1, 3) and (2, -4, 11) on the line joining the points (-1, 2, 3) and (3, -2, 10) is

[2020]

Correct Ans: 8

JEE Main Math Vector Questions No: 107

Let a, b and c be three unit vectors such that | a b |² +| āc |² = 8. Then | ā + 2b |² + | ā + 2c |² is equal to

[2020]

Correct Ans: 2

JEE Main Math Vector Questions No: 108

Let the vectors a, b, c be such that | ā | = 2, | b | = 4 and | c | = 4. If the projection of b on a is equal to the projection of c on a and b is perpendicular to c, then the value of | a + b c | is

[2020]

Correct Ans: 6

JEE Main Math Vector Questions No: 109

If x and y be two non-zero vectors such that | x + y | = | x | and 2x + ????y is perpendicular to y, then the value of ???? is

[2020]

Correct Ans: 1

JEE Mains Vector Questions No: 110

If a and b are unit vectors, then the greatest value of √3 | a + b | + | a b | is

[2020]

Correct Ans: 4

JEE Main Math Vector Questions No: 111

If the vectors, p = (a + 1)i + aj + ak, q = ai + (a + 1)j +ak and r = ai + aj + (a + 1)k (a ∈ R) are coplanar and 3 (p ∙ q)² – λ | r × q |² = 0, then the value of λ is

[2020]

Correct Ans: 1

JEE Main Math Vector Questions No: 112

Let the position vectors of points ‘A’ and ‘B’ be i + j + k and 2i + j + 3k, respectively. A point ‘P’ divides the line segment AB internally in the ratio λ : 1 (λ > 0). If O is the region and OB × OP – 3 | OA × OP |2 = 6, then λ is equal to

[2020]

Correct Ans: 0.8

JEE Mains Math Vector Questions No: 113

Let a, b, c ∈ R be such that a² + b² + c² = 1. If acosθ – bcos(θ  + 2π/3) = c cos(θ + 4π/3)  where θ = (π/9), then the angle between the vectors ai + bj + ck and bi + cj + ak is

[2020]

Option A: (π / 2)

Option B: (2π / 3)

Option C: (π / 9)

Option D: 0

Option A: (π / 2)

JEE Main Math Vector Questions No: 114

If a and b are perpendicular, then a × (a × (a × (a × b) ) ) is equal to :

[2021]

Option A: a × b

Option B: 0

Option C: (1/2) | a |4 b

Option D: | a |4 b

Option D: | a |4 b

JEE Main Math Vector Questions No: 115

Let c be a vector perpendicular to the vectors a = i + j k and b = i + 2j + k. If c ∙ (i + j + 3k) = 8 then the value of c ∙ (a × b) is equal to

[2021]

Correct Ans: 28

JEE Main Math Vector Questions No: 116

Let a = i + 2j – 3k and b = 2i – 3j + 5k. If r × a = b × r, r ∙ (ai + 2j + k) = 3 and r ∙ (2i + 5j – αk) = 1 α ∈ R, then the value of α +| r |2 is equal to:

[2021]

Option A: 15

Option B: 13

Option C: 9

Option D: 11

Option A: 15

JEE Main Math Vector Questions No: 117

Let a = 2i – 3j + 4k and b = 7i + j – 6k. If r × a b × r, r (i + 2j+ k) = −3, then r (2i – 3j + k)

[2021]

Option A: 10

Option B: 13

Option C: 8

Option D: 12

Option D: 12

JEE Mains Math Vector Questions No: 118

Let a = i – αj + βk, b = 3i + βj – αk and c = – αi – 2j + k, where α and β are integers. If a ∙ b = -1 and b ∙ c = 10, then (a × b) c is equal to

[2021]

Correct Ans: 9

JEE Main Math Vector Questions No: 119

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

[2021]

Option A: -2

Option B: -6

Option C: 6

Option D: 2

Option A: -2

JEE Vector Questions No:120

Let a = i + 5j + αk, b = i + 3j + βk and c = −i + 2j – 3k be three vectors such that, | b × c | = 5√3 and a is perpendicular to b. Then the greatest amongst the values of | a |² is

[2021]