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 Math Vectors Questions Answer Keys Solutions.
JEE Mains Mathematics Vectors Questions Bank
JEE Main Vector Questions No: 121
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 } + c × { (r – a) × c } =0, then r is equal to
[2021]
Option A: (1/3) (a + b + c)
Option B: (1/3) (2a + b – c)
Option C: (1/2) (a + b + c)
Option D: (1/2) (a + b + 2c)
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Option C: (1/2) (a + b + c)
JEE Mains Math Vector Questions No: 122
A line ‘l’ passing through origin is perpendicular to the line I1 : r = (3 + t)i + (1 + 2t)j + (4 + 2t)k ,I2 : r = (3 + 2s)i + (3 + 2s)j + (2 + s)k. If the co-ordinates of the point in the first octant on ‘l2‘ at a distance of √17 from the point of intersection of ‘I’ and ‘I1‘ are (a, b, c) then 18(a + b + c) is equal to
[2021]
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Correct Ans: 44
JEE Main Math Vector Questions No: 123
Let a = i + aj + 3k and 3i – aj + k. If the area of the parallelogram whose adjacent sides are represented by the vectors a and b is 8√3 square units, then a ∙ b is equal to
[2021]
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Correct Ans: 2
JEE Vector Questions No:124
Let a = i + 2j – k, b = i – j and c = i – j – k be three given vectors, if r is a vector such that r × a = c × a and r ∙ b = 0, then r ∙ a is equal to
[2021]
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Correct Ans: 12
JEE Main Vector Questions No: 125
If a = αi + βj + 3k, b = -βi – αj – k and c = i – 2j – k such that a · b = 1 and b · c = −3, then (1/3) ((a × b) ∙ c) is equal to
[2021]
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Correct Ans: 2
JEE Mathematics Vector Questions No: 126
In a triangle ABC, if | BC | = 8, | CA | = 7, | AB | = 10, then the projection of the vector | AB | on | AC | is equal to :
[2021]
Option A: (115 / 16)
Option B: (25 / 4)
Option C: (127 / 20)
Option D: (85 / 14)
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Option D: (85 / 14)
JEE Mathematics Vector Questions No: 127
If (a + 3b) is perpendicular to (7a – 5b) and (a – 4b) is perpendicular to (7a – 2b), then the angle between a and b (in degrees) is
[2021]
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Correct Ans: 60
Vector JEE Questions No: 128
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 vector a × c is l, then the value of 3l² is equal to
[2021]
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Correct Ans: 2
Vector JEE Main Questions No: 129
If the projection of the vector i + 2j + k on the sum of the two vectors 2i + 4j – 5k and –????i + 2j + 3k is 1, then ???? is equal to
[2021]
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Correct Ans: 5
JEE Main Math Vector Questions No: 130
Let three vectors a, b and c be such that c is coplanar with a and b, a ∙ c = 7 and b is perpendicular to c, where a = – i + j + k and b = 2i + k, then the value of 2 | a + b + c |2 is
[2021]
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Correct Ans: 75
JEE Main Math Vector Questions No:131
If vectors a1 = xi – j + k and a2 = i + yj + zk are collinear, then a possible unit vector parallel to the vector xi + yj + zk is
[2021]
Option A: (1 / √3) (i – j + k)
Option B: (1 / √3) (i + j – k)
Option C: (1 / √2) (i – j)
Option D: (1 / √2) (-j + k)
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Option A: (1 / √3) (i – j + k)
JEE Main Vector Questions No: 132
Let the position vectors of two points P and Q be 3i – j + 2k and i + 2j – 4k, respectively. Let R and S be two points such that the direction ratios of lines PR and QS are (4, -1, 2) and (-2, 1, -2), respectively. Let lines PR and QS intersect at T. If the vector TA is perpendicular to both PR and QS and the length of vector TA is √5 units, then the modulus of a position vector of A is:
[2021]
Option A: √482
Option B: √227
Option C: √5
Option D: √171
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Option D: √171
JEE Mathematics Vector Questions No: 133
Let O be the origin. Let OP = xi + yj – k and OQ = –i + 2j + 3xk, x, y ∈ R, x > 0, be such that | PQ |= √20 and the vector OP is perpendicular to OQ. If OR = 3i + zj – 7k, z ∈ R, is coplanar with OP and OQ, then the value of x² + y2 + z² is equal to
[2021]
Option A: 7
Option B: 9
Option C: 2
Option D: 1
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Option B: 9
JEE Mathematics Vector Questions No: 134
For p > 0, a vector V2 = 2i + (p + 1)j by obtained by rotating the vector V1 = √3pi + j by an angle θ about origin in counter clockwise direction. If tan θ = (α√3 – 2) / (4√3 + 3)), then the value of α is equal to
[2021]
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Correct Ans: 6
Vector JEE Questions No: 137
Let a, b, c be three mutually perpendicular vectors of the same magnitude and equally inclined at an angle θ, with the vector a + b + c. Then 36cos22θ is equal is
[2021]
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Correct Ans: 4
Vector JEE Main Questions No: 136
Let a vector a be coplanar with vectors b = 2i + j + k and c = i – j + k. If a is perpendicular to d = 3i + 2j + 6k and | a | = √10. Then a possible value of [a b c] + [a b d] + [a c d] is equal to :
[2021]
Option A: -42
Option B: -40
Option C: -29
Option D: -38
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Option A: –42
JEE Main Math Vector Questions No: 137
Let be two vectors. If p = 2i + 3j + k and q = i + 2j + k vector r = (αi + βj + γk) is perpendicular to each of the vectors (p + q) and (p – q), and | r | = √3, then | α | + | β | + | γ | is equal to
[2021]
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Correct Ans: 3
JEE Main Math Vector Questions No: 138
Let a and b be two vectors such that | 2a + 3b | = |3a + b| and the angle between a and b is 60°. If (1/8)a is a unit vector, | b | then is equal to :
[2021]
Option A: 4
Option B: 6
Option C: 5
Option D: 8
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Option C: 5
JEE Main Math Vector Questions No: 139
Let a = 2i – j + 2k and b = i + 2j – k. Let a vector v be in the plane containing a and b. If v is perpendicular to the vector 3i + 2j – k and its projection on a is 19 units, then | 2v |² is equal to
[2021]
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Correct Ans: 1494
| 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 | |
