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# JEE Main Mathematics 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 Mathematics Vectors Questions Answer Keys Solutions.

### JEE Mains Mathematics Vectors Questions Bank

JEE Mathematics Vector Questions No: 31

If C is the mid point of AB and P is any outside AB, then



Option A: PA PB = 2PC

Option B:  PA PB = PC

Option C:  PA PB + 2PC = 0

Option D:  PA PB + PC = 0

Option A: PA + PB = 2PC

JEE Main Math Vector Questions No: 32

The value of a, for which the points A, B. C with position  vectors  2–  jk, –  3j – 5k, and a–  3jk, respectively are the vertices of a right-angled triangle with C = (π/2) are



Option A: 2 and 1

Option B: –2 and -1

Option C: –2 and 1

Option D: 2 and -1

Option A: 2 and 1

Vector JEE Questions No: 33

A particle has tow velocities of equal magnitude inclined to each other at an angle  θ. If one of them is heated the angle between the other and the origin resultant velocity is bisected by the new resulted. Then  θ is



Option A: 90o

Option B: 120o

Option C: 40o

Option D: 60o

Option B: 120o

Vector JEE Main Questions No: 34

If (a × b) × × (b × c) where a , b, c  are any three vectors such ab ≠ 0 bc ≠ 0 then  and  are



Option A: Inclined at an angle of (π/3) between them

Option B: Inclined at an angle of (π/6) between them

Option C: Perpendicular

Option D: Parallel

Option D: Parallel

Vector Questions for JEE Mains Questions No: 35

ABC  is a triangle right angled at A. The resultant of the forces acting along AB, AC with magnitudes 1/AB and 1/AC respectively is the force along AD, where D is the foot of the perpendicular from A onto BC. The magnitude of the resultant is



Option A: ( AB2 + AC2 / (AB2) (AC2) )

Option B: ( (AB) (AC) / AB + AC )

Option C: (1/AB) + (1/AC)

Vector JEE Math Questions No: 36

If  and  are unit and  θ is the acute angle between them, then 2 θ > 3 θ is a unit vector for



Option A: Exactly two values of  θ

Option B: More than two values of  θ

Option C: No value of  θ

Option D: Exactly one values of  θ

Option D: Exactly one values of  θ

JEE Vector Questions No:37

Let a i + j + k , b = i j + 2k and c = xi + (x-2)j k. If the vector  c lies in the plane of a and b then x equals



Option A: -4

Option B: -2

Option C: 0

Option D: 1

Option B: -2

Vector for JEE Main Questions No: 38

The non-zero vectors a, b and c are related by a = 8b and c= -7b . Then the angle between a and c is



Option A:0

Option B: π/4

Option C: π/2

Option D: π

Option D: π

JEE Mains Vector Questions No: 39

The vector a = αi + 2j + βk lies in the plane of the vectors b = ij and c = jk and bisects the angle between b and c .Then which one of the following gives possible values of α and  β?



Option A: α = 2, β = 2

Option B: α = 1, β = 2

Option C: α = 2, β = 1

Option D: α = 1, β = 1

Option D: α = 1, β = 1

JEE Mains Math Vector Questions No: 40

If u, v, w are non-coplanar vectors and p, q are real numbers, then the equality [ 3u  pv  pw ] –  [ pv qu ] – [ 2w  q qu ] = 0 holds for



Option A: Exactly one value of (p,q)

Option B: Exactly two value of (p,q)

Option C: More than two but not all values of (p,q)

Option D: All values of (p,q)

Option A:Exactly one value of (p,q)

Vector Questions for JEE Questions No: 41

Let aj –  k and c = i – j – k. Then vector b satisfying a × b + c = 0 and a × b = 3 is



Option A: 2i – j + 2k

Option B: i – j – 2k

Option C: i + j – 2k

Option D: –i + j – 2k

Option D: i + j – 2k

JEE Vector Questions No:42

If the vectors a = i j + 2k, b = 2i + 4j + k and c = ????i + j +μ ֝k are mutually orthogonal, then (????, μ) =



Option A: (2,-3)

Option B: (-2,3)

Option C: (3,-2)

Option D: (-3,2)

Option D: (-3,2)

JEE Mathematics Vector Questions No: 43

If the vectors ā = ib + 2k, b = 2i + 4j + k and c = ????i + j + μk are mutually orthogonal, then (????,μ) =



Option A: (2, -3)

Option B: (-2, 3)

Option C: (3, -2)

Option D: (-3, 2)

Option D: (-3, 2)

JEE Main Vector Questions No: 44

Let a, b, c be three non-zero vectors which are pairwise non-collinear. If a +3b is collinear with c and b + 2c is collinear with a , then a + 3b + 6c is



Option A: 0

Option B: c

Option C: a

Option D: c

Option A: 0

JEE Mathematics Vector Questions No: 45

If the vectors pi + j + k, i + qj + k and i + j + rk (p ≠ q ≠ r ≠ 1) are coplanar, then the value of pqr – (p + q + r) is



Option A: -1

Option B: -2

Option C: 2

Option D: 0

Option B: -2

JEE Main Vector Questions No: 46

If = (1/√10) (3k) and = (1/7) (2+ 3– 6k), then the value of (2– 2b) [ (a x b) x (+ 2b) ] is



Option A: -3

Option B: 5

Option C: 3

Option D: -5

Option D: -5

JEE Mathematics Vector Questions No: 47

The vectors  and  are not perpendicular and  and  are two vectors satisfying b x c b x d and  a ∙ d = 0. Then the vector  is equal to



Option A : Option B: Option C: Option D: Option C: C

JEE Main Math Vector Questions No: 48

Let ABCD be a parallelogram such that AB = q, AD = p and ∠BAD be an acute angle. If r is the vector that coincides with the altitude directed from the vertex B to the side AD, then is



Option A: – [( p q )/( p  p )] p

Option B: = -3q + [3 (p  q) / (p  p)] p

Option C: = 3– [3(p q )/(p p)] p

Option D: = –+ [(p q) / (p p)] p

Option D: r  = -q + [(p q / p  p)] p

Vector JEE Questions No: 49

Let a and b be two unit vectors. If the vectors c = a + 2b and d = 5a – 4b are perpendicular to each other, then the angle between a and b is



Option A: π/3

Option B: π/4

Option C: π/6

Option D: π/2

Option A: π/3

JEE Main Math Vector Questions No: 50

If – 2+ 3k, b = 2i + 3j and c = ????i + + (2???? – 1) are coplanar vectors , then ???? is equal to



Option A: 0

Option B: -1

Option C: 2

Option D: 1

Option A: 0

JEE Mains Vector Questions No: 51

If a = i – 2j + 3k, b = 2î + 3j k and c = ri + j + (2r – 1)k are three vectors such that c is parallel to the plane of a and b, then r is equal to



Option A: 1

Option B: -1

Option C: 0

Option D: 2

Option C: 0

Vector JEE Questions No: 52

Statement I : If the points (1, 2, 2) (2, 1, 2) (2, 2, z) (1, 1, 1) are coplanar, then z=2

Statement II: If the 4 points P, Q, R and S are coplanar, then the volume of the tetrahedron PQRS is 0



Option A: Statement I is false Statement II is true

Option B: Statement I is true Statement II is false

Option C: Statement I is true Statement II is true, Statement II is a correct explanation of Statement I

Option D: Statement I is false Statement II is true, Statement II is not a correct explanation of Statement I

Option A: Statement I is false Statement II is true

Vector JEE Main Questions No: 53

If u =  + 4k, v =  i + 3k  and w = cosθ + sinθ are vectors in 3 dimensional space, then the maximum value of |u × v  w| is



Option A: √3

Option B: 5

Option C: √14

Option D: 7

Option B: 5

Vector Questions for JEE Mains Questions No: 54

Statement I : The vectors aand lie in the same plane if and only if a ( b × c )= 0

Statement II : The vectors u and are perpendicular if and only if u ∙ = 0 where u × v is a perpendicular to the plane of and v



Option A: Statement I is false Statement II is true

Option B: Statement I is true Statement II is true, Statement II is a correct explanation for Statement I

Option C: Statement I is true Statement II is false

Option D: Statement I is true Statement II is true, Statement II is not a correct explanation for Statement I

Option C: Statement I is true Statement II is false

Vector JEE Questions No: 55

ABCD is parallelogram. The position vectors of A and C are respectively, 3i + 3j + 5k and i – 5j – 5k. If M is the midpoint of the diagonal DB, then the magnitude of the projection of OM on OC, where O is the origin, is



Option A: 7√51

Option B: (7 / √50)

Option C: 7√50

Option D: (7 / √51)

Option D: (7 / √51)

Vector JEE Main Questions No: 56

A unit vector which is perpendicular to the vector 2i j + 2k and is coplanar with the vectors i + jk and 2i + 2j k is



Option A: (2j + k) / √5

Option B: (3i + 2j – 2k ) / √17

Option C:  (3i + 2j + 2k) / √17

Option D: (2i + 2j – 2k) / 3

Option D: (2i + 2j − 2k ) / 3

Vector Questions for JEE Mains Questions No: 57

If a + b + c = 0, | a | = 3, | b | = 5, and | c | = 7, then the angle between  and  is



Option A: π/3

Option B: π/4

Option C: π/6

Option D: π/2

Option A: π/3

Vector JEE Main Questions No: 58

If the vectors AB = 3i + 4k and AC = 5i – 2j + 4k are the sides of a triangle ABC, then the length of the median through A is



Option A: √72

Option B: √33

Option C: √45

Option D: √18

Option B: √33

Vector Questions No: 59

The vector (i  × a ∙ b) + (j  × a ∙ b)+ (k  × a ∙ b) is equal to



Option A: × a

Option B: a

Option C: a ×

Option D:

Option C: a ×

Vector Questions No: 60

Let a = 2i + j – 2k and b j . Let c be a vector such that a ∙ c = | c | = 3, | c a | = 2√2 and the angle between c and a  × b be 30°. Then | (a × b) × c | is equal to:



Option A: (1 / 2)

Option B: (3√3 / 2)

Option C: 3

Option D: (3 / 2)