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
Show/Hide Answer Key
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
Show/Hide Answer Key
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
Show/Hide Answer Key
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
Show/Hide Answer Key
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)
Show/Hide Answer Key
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
Show/Hide Answer Key
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
Show/Hide Answer Key
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)
Show/Hide Answer Key
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
Show/Hide Answer Key
Option C: (-1 / 2)
JEE Mathematics Vector Questions No: 100
Let a, b 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]
Show/Hide Answer Key
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]
Show/Hide Answer Key
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
Show/Hide Answer Key
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
Show/Hide Answer Key
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
Show/Hide Answer Key
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)
Show/Hide Answer Key
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]
Show/Hide Answer Key
Correct Ans: 8
JEE Main Math Vector Questions No: 107
Let a, b and c be three unit vectors such that | a − b |² +| ā − c |² = 8. Then | ā + 2b |² + | ā + 2c |² is equal to
[2020]
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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]
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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]
Show/Hide Answer Key
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]
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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]
Show/Hide Answer Key
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]
Show/Hide Answer Key
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
Show/Hide Answer Key
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
Show/Hide Answer Key
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]
Show/Hide Answer Key
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
Show/Hide Answer Key
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
Show/Hide Answer Key
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]
Show/Hide Answer Key
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
Show/Hide Answer Key
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]
Show/Hide Answer Key
Correct Ans: 90
| JEE Main Mathematics Previous Year Questions with Solutions: Algebra |
| JEE Main Previous Year Mathematics Questions Set, Relations & Functions | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |
| JEE Main Previous Year Mathematics Questions Complex Numbers | 1 to 30 | 31 to 60 | 61 to 81 | |
| JEE Main Previous Year Mathematics Questions Sequence & Series | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |
| JEE Main Previous Year Mathematics Questions Quadratic Equations | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |
| JEE Main Previous Year Mathematics Questions Permutations & Combinations | 1 to 30 | 31 to 60 | 61 to 94 | |
| JEE Main Previous Year Mathematics Questions Binomial Theorems | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |
| JEE Main Previous Year Mathematics Questions Determinants & Matrices | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |
| JEE Main Mathematics Previous Year Questions with Solutions: Trigonometry |
| JEE Main Previous Year Mathematics Questions Trigonometry Ratios Identities | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |
| JEE Main Previous Year Mathematics Questions Properties of Triangles | 1 to 31 | |
| JEE Main Previous Year Mathematics Questions Trigonometrical Equations | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |
| JEE Main Previous Year Mathematics Questions Inverse Trigonometrical Functions | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |
| JEE Main Previous Year Mathematics Questions Height & Distance | 1 to 27 | |
| JEE Main Mathematics Previous Year Questions with Solutions: Coordinate Geometry |
| JEE Main Previous Year Mathematics Questions Cartesian System & Straight Lines | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |
| JEE Main Previous Year Mathematics Questions Circles | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |
| JEE Main Previous Year Mathematics Questions Parabola | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |
| JEE Main Previous Year Mathematics Questions Ellipse | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |
| JEE Main Previous Year Mathematics Questions Hyperbola | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |
| JEE Main Mathematics Previous Year Questions with Solutions: Differential Equations |
| JEE Main Previous Year Mathematics Questions Limit, Continuity & Differentiability | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |
| JEE Main Previous Year Mathematics Questions Differentiations | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |
| JEE Main Previous Year Mathematics Questions Application of Derivative | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |
| JEE Main Mathematics Previous Year Questions with Solutions: Integral Calculus |
| JEE Main Previous Year Mathematics Questions Indefinite Integrals | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |
| JEE Main Previous Year Mathematics Questions Definite Integrals | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |
| JEE Main Previous Year Mathematics Questions Area By Integration | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |
| JEE Main Mathematics Previous Year Questions with Solutions: Differential Equations |
| JEE Main Previous Year Mathematics Questions Differential Equations | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |
| JEE Main Mathematics Previous Year Questions with Solutions: Vector & 3D Geometry |
| JEE Main Previous Year Mathematics Questions Vectors | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 139 | |
| JEE Main Previous Year Mathematics Questions 3D Geometry | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |
| JEE Main Mathematics Previous Year Questions with Solutions: Statistics & Probability |
| JEE Main Previous Year Mathematics Questions Statistics | 1 to 30 | 31 to 60 | 61 to 86 | |
| JEE Main Previous Year Mathematics Questions Probability | 1 to 30 | 31 to 60 | 61 to 95 | |
| JEE Main Mathematics Previous Year Questions with Solutions: Miscellaneous |
| JEE Main Previous Year Mathematics Questions Mathematical Induction | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |
| JEE Main Previous Year Mathematics Questions Mathematical Reasoning | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |
