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# JEE 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 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



Option A: (1/3) (+ c)

Option B: (1/3) (2+ b c)

Option C: (1/2) (+ c)

Option D: (1/2) (+ + 2c)

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



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



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



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



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 :



Option A: (115 / 16)

Option B: (25 / 4)

Option C: (127 / 20)

Option D: (85 / 14)

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



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



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



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



Correct Ans: 75

JEE Main Math Vector Questions No:131

If vectors a1 = xi j + k and a2i + yj + zk are collinear, then a possible unit vector parallel to the vector xi + yj + zk is



Option A: (1 / √3) (i j + k)

Option B: (1 / √3) (i + jk)

Option C: (1 / √2) (i j

Option D: (1 / √2) (-j + k)

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:



Option A: √482

Option B: √227

Option C: √5

Option D: √171

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



Option A: 7

Option B: 9

Option C: 2

Option D: 1

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



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



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 :



Option A: -42

Option B: -40

Option C: -29

Option D: -38

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



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 :



Option A: 4

Option B: 6

Option C: 5

Option D: 8

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