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# JEE Math Previous Year Paper 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 Previous Year Paper Vectors Questions Answer Keys Solutions.

### JEE Mains Mathematics Vectors Questions Bank

Vector Questions No: 61

Let a = 2i j + k, b = i + 2j k and c = i + j – 2k be three vectors. A vector of the type b + ????c for some scalar ????, whose projection on a is of magnitude (√2 / √3) is

[2013]

Option A: 2i + j + 5k

Option B: 2i + 3j – 3k

Option C: 2i j + 5k

Option D: 2i + 3j + 3k

Option B: 2i + 3j – 3k

JEE Main Math Vector Questions No: 62

If a, b and c are unit vectors satisfying a – √3b + c = 0, then the angle between the vectors a and c is:

[2013]

Option A: π/4

Option B: π/3

Option C: π/6

Option D: π/2

Option B: π/3

JEE Mains Math Vector Questions No: 63

If a and b are non-collinear vectors, then the value of α for which the vectors u = (α – 2)a + b and v = (2 + 3α)a – 3b are collinear is

[2013]

Option A: 3/2

Option B: 2/3

Option C: -3/2

Option D: -2/3

Option B: 2/3

JEE Main Math Vector Questions No: 64

If [a × b  b × c  c × a ]= k[a  b  c]2, then ???? is equal to

[2014]

Option A: 2

Option B: 3

Option C: 0

Option D: 1

Option D: 1

JEE Mains Vector Questions No: 65

If | c |2 = 60  and × ( i + 2j + 5k) = 0, then a value of c (-7i + 2j + 3k) is

[2014]

Option A: 4√2

Option B: 12

Option C: 24

Option D: 12√2

Option D: 12√2

JEE Mains Math Vector Questions No: 66

If =  3i – 6jk, y = i + 4j – 3k, and z =  3i – 4j – 12k, then the magnitude of the projection of x × on  is

[2014]

Option A: 12

Option B: 15

Option C: 14

Option D: 13

Option C: 14

JEE Main Math Vector Questions No: 67

If [ × b  b × c  c × a ] = ???? [ a b c ]then ???? is equal to

[2014]

Option A: 0

Option B: 1

Option C: 2

Option D: 3

Option B: 1

JEE Mains Vector Questions No: 68

If | a | = 2, | b | = 3 and | 2a b | = 5 then | 2a + b | equals

[2014]

Option A: 17

Option B: 7

Option C: 5

Option D: 1

Option C: 5

JEE Mains Math Vector Questions No: 69

If x, y and z are three unit vectors in three-dimensional space, then the minimum value of | x + y |2 + | y + z |2 + | z + x |2

[2014]

Option A: (3 / 2)

Option B: 3

Option C: 33

Option D: 6

Option B: 3

JEE Main Math Vector Questions No: 70

Let a, b and  be three non-zero vectors such that no two of them are collinear and (a × b) × c = (1/3) | b | | c | | a | . If θ is the angle between vectors b and c , then a value of sinθ is :

[2015]

Option A: -√2/3

Option B: 2/3

Option C: -2√3/3

Option D: 2√2/3

Option D: 2√2/3

JEE Main Math Vector Questions No: 71

In a parallelogram ABD, | AB | = a, | AD | = b and | AC | = c, then DA ∙ AB has the value

[2015]

Option A: (1/2) (a² + b² + c²)

Option B: (1/2) (a² − b² + c²)

Option C: (1/2) (a² + b² – c²)

Option D: (1/3) (b² + c² – a²)

Option C: (1/2) (a² + b² – c²)

JEE Vector Questions No:72

Let and be two unit vectors such that | a + b |= √3. If + 2+ 3(a × b) then 2 | c | is equal to

[2015]

Option A: √55

Option B: √37

Option C: √51

Option D: √43

Option A: √55

JEE Main Math Vector Questions No: 73

Let a, b and c be three unit vectors such that a x (b × c) = (3/2) (b + c) . If b is not parallel to c, then the angle between a and b is:

[2016]

Option A: π/2

Option B: /3

Option C: /6

Option D: /4

Option C: 5π/6

JEE Main Math Vector Questions No:74

In a triangle ABC, right angled at the vertex A, if the position vectors of A, B and C are respectively 3i + j k, –i + 3j + pk and 5i + qj – 4k, then the point (p,q) lies on a line:

[2016]

Option A: Making an obtuse angle with the positive direction of x-axis

Option B: Parallel to x-axis

Option C: Parallel to y-axis

Option D: Making an acute angle with the positive direction of x-axis

Option D: Making an acute angle with the positive direction of x-axis

JEE Main Math Vector Questions No: 75

Let ABC be a triangle whose circumcentre is at P. If the position vectors A, B, C and P are a, b, c and a + b + c / 4 respectively, then the position vector of the orthocentre of this triangle, is

[2016]

Option A: -(a + b + c) / 2

Option B: (a + b + c )

Option C: (a + b + c) / 2

Option D: 0

Option C: (a + b + c) / 2

JEE Mains Vector Questions No: 76

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

[2017]

Option A: 25/8

Option B: 2

Option C: 5

Option D: 1/8

Option B: 2

JEE Main Vector Questions No: 77

The area (in sq. units) of the parallelogram whose diagonals are along the vectors 8i – 6j and 3i + 4j – 12k, is:

[2017]

Option A: 26

Option B: 65

Option C: 20

Option D: 52

Option B: 65

JEE Mathematics Vector Questions No: 78

If the vector b = 3j + 4k is written as the sum of a vector b1, parallel to a = i + j and a vector b2, perpendicular to a, then b1 × b2 is equal to

[2017]

Option A: – 3i + 3j – 9k

Option B: 6i – 6j + (9/2) k

Option C: – 6i + 6j – (9/2) k

Option D: 3i – 3j + 9k

Option B: 6i – 6j + (9/2) k

JEE Main Math Vector Questions No: 79

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

[2017]

Option A: (1 / 8)

Option B: (25 / 8)

Option C: 2

Option D: 5

Option C: 2

JEE Mains Math Vector Questions No: 80

Let u be a vector coplanar with the vectors a =  2+ 3jk and b = j + k . If u is perpendicular to a and b = 24 , then 2πr = n ????n is equal to :

[2018]

Option A: 84

Option B: 336

Option C: 315

Option D: 256

Option B: 336

Vector JEE Questions No: 81

If a, b, and c are unit vectors such that a + 2b + 2c = 0, then | a × c | is equal to

[2018]

Option A: (1 / 4)

Option B: (√15 / 4)

Option C: (15 / 16)

Option D: (√15 / 16)

Option B: (√15 / 4)

Vector JEE Main Questions No: 82

Let a = i + j + k , c = j k and a vector b be such that a × b = c and ā b = 3. Then | b | equals?

[2018]

Option A: (√11 / √ 3)

Option B: (√11 / 3)

Option C: (11 / √3)

Option D: (11 / 3)

Option A: (√11 / √ 3)

JEE Main Math Vector Questions No: 83

If the position vectors of the vertices A, B and C of a ABC are respectively 4i +7j + 8k, 2i + 3j + 4k and 2i + 5j + 7k, then the position vector of the point, where the bisector of A meets BC is

[2018]

Option A: (1 / 2) (4i + 8j + 11k)

Option B: (1 / 3) (6i + 13j + 18k)

Option C: (1 / 4) (8î + 14ĵ + 9k

Option D: (1 / 3) (6i +11j + 15k)

Option B: (1 / 3) (6i + 13j + 18k)

JEE Main Math Vector Questions No: 84

Let a = i j, b = i + j + k and c be a vector such that a × c + b = 0 and a ∙ c = 4, then | c |2 is equal to:

[2019]

Option A: (19 / 2)

Option B: 9

Option C: 8

Option D: (17 / 2)

Option A: 19/2

JEE Main Math Vector Questions No: 85

Let a, b and c be three unit vectors, out of which vectors b and c are non-parallel. If α and β are the angles which vector ā makes with vectors b and c respectively and a × (b × c) = (1/2) b, then | α – β | is equal to :

[2019]

Option A: 300

Option B: 900

Option C: 600

Option D: 450

Option A: 300

JEE Mains Vector Questions No: 86

Let a = 3i + 2j + xk and b = i j + k, for some real x. Then | a × | = r is possible if:

[2019]

Option A:

Option B:

Option C

Option D

Option B: B

JEE Mains Math Vector Questions No: 87

The magnitude of the projection of the vector 2i + 3j + k on the vector perpendicular to the plane containing the vectors î + j + k and î + 2j + 3k, is

[2019]

Option A: (√3 / 2)

Option B: √6

Option C: 3√6

Option D: (√3 / √2)

Option D: (√3 / √2)

JEE Main Math Vector Questions No: 88

Let α = 3i + j and β = 2i – 3j + 3k. If β = β₁ – β₂, where β₁ is parallel to α and β2 is perpendicular to α, then β₁ × β₂ is equal to:

[2019]

Option A: -3i + 9j + 5k

Option B: 3i – 9j – 5k

Option C: (1 / 2) ( -3i + 9j + 5k )

Option D: (1 / 2) ( 3i – 9j – 5k )

Option C: (1 / 2) ( -3i + 9j + 5k )

JEE Main Vector Questions No: 89

Let a = i + j + √2k, b = b₁i + b₂j + √2k and c = 5i + j + √2k be three vectors such that the projection vector of b on ā is ā.

If a + b is perpendicular to c, then | b | is equal to:

[2019]

Option A: √32

Option B: 6

Option C: √22

Option D:

Option B: 6

JEE Mathematics Vector Questions No: 90

Let ā = 2i + λ₁j + 3k, b = 4i + (3 − λ₂)j + 6k and c = 3i + 6j + (λ3 – 1)k be three vectors such that b = 2a and a is perpendicular to c. Then a possible value of (λ, λ₂, λ3) is

[2019]

Option A: (1, 3, 1)

Option B: (-1 / 2, 4, 0)

Option C: (1 / 2, 4, -2)

Option D: (1, 5, 1)