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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

Show/Hide Answer Key

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

Show/Hide Answer Key

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

Show/Hide Answer Key

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

Show/Hide Answer Key

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

Show/Hide Answer Key

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

Show/Hide Answer Key

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

Show/Hide Answer Key

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

Show/Hide Answer Key

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

Show/Hide Answer Key

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

Show/Hide Answer Key

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)

Show/Hide Answer Key

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

Show/Hide Answer Key

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

Show/Hide Answer Key

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 

Show/Hide Answer Key

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

Show/Hide Answer Key

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

Show/Hide Answer Key

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

Show/Hide Answer Key

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

Show/Hide Answer Key

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

Show/Hide Answer Key

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

Show/Hide Answer Key

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)

Show/Hide Answer Key

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)

Show/Hide Answer Key

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)

Show/Hide Answer Key

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)

Show/Hide Answer Key

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

Show/Hide Answer Key

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

Show/Hide Answer Key

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)

Show/Hide Answer Key

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 )

Show/Hide Answer Key

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:

Show/Hide Answer Key

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)

Show/Hide Answer Key

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

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 |

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