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** = 2**i **– **j **+ **k**,** b **= **i **+ 2**j **– **k** and **c **= **i **+ **j **– 2**k** 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**: 2**i **+ **j **+ 5**k**

**Option B**: 2**i **+ 3**j **– 3**k**

**Option C**: 2**i **– **j **+ 5**k**

**Option D**: 2**i** + 3**j **+ 3**k**

**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 **– √3**b **+ **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 **– 3**b** 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 **c ****×** (** i** + 2**j **+ 5**k**) = **0**, then a value of **c** **∙** (-7**i** + 2**j **+ 3**k**) 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 **x **= 3**i** – 6**j** – **k, y **= **i** +** 4j **– 3**k,** and **z **= 3**i** – 4**j** – 12**k, **then the magnitude of the projection of **x **×** y ** on **z ** 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 [ **a ****× b b** × **c c ****× a **] = ???? [ **a b c **]^{2 }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 | 2**a **– **b **| = 5 then | 2**a **+ **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**: 3√3

**Option D**: 6

**Show/Hide Answer Key**

**Option B: 3**

**JEE Main Math Vector Questions No: 70**

Let **a**, **b **and **c ** 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 **a ** and **b **be two unit vectors such that | **a **+ **b **|= √3. If **c **= **a **+ 2**b **+ 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**: 2π/3

**Option C**: 5π/6

**Option D**: 3π/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 3**i **+ **j **– **k**, –**i **+ 3**j **+ p**k** and 5**i **+ q**j **– 4**k**, 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 – 2**i** +** j** – 2**k** and **b **= **i **+ **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 8**i **– 6**j** and 3**i **+ 4**j **– 12**k**, 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 **= 3**j **+ 4**k** is written as the sum of a vector **b**_{1}, parallel to** a **= **i **+ **j** and a vector **b**_{2}, perpendicular to **a**, then **b**_{1 }× **b**_{2} is equal to

**[2017]**

**Option A**: – 3**i **+ 3**j **– 9**k**

**Option B**: 6i – 6**j **+ (9/2) **k**

**Option C**: – 6**i **+ 6**j **– (9/2) **k**

**Option D**: 3**i **– 3**j **+ 9**k**

**Show/Hide Answer Key**

**Option B: 6i – 6j + (9/2) k**

**JEE Main Math Vector Questions No: 79**

Let **ā** = 2î +** j** – 2**k** 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**i **+ 3**j** – **k** and **b** = **j** + **k** . If **u** is perpendicular to **a** and **u **∙ **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 **+ 2**b **+ 2**c **= **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 4**i** +7**j** + 8**k**, 2**i** + 3**j **+ 4**k** and 2**i** + 5**j** + 7**k**, then the position vector of the point, where the bisector of ∠ A meets BC is

**[2018]**

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

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

**Option C**: (1 / 4) (8î + 14ĵ + 9**k**)

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

**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**: 30^{0}

**Option B**: 90^{0}

**Option C**: 60^{0}

**Option D**: 45^{0}

**Show/Hide Answer Key**

**Option A: 30 ^{0}**

**JEE Mains Vector Questions No: 86**

Let **a **= 3**i **+ 2**j **+ x**k** and **b **= **i **– **j **+ **k**, for some real x. Then | **a** × **b **| = 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 2**i **+ 3**j **+ **k** on the vector perpendicular to the plane containing the vectors **î **+ **j **+ **k** and î + 2**j** + 3**k**, 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** = 3**i **+ **j** and **β **= 2**i **– 3**j **+ 3**k.** If **β **= **β**₁ – **β**₂, where **β**₁ is parallel to **α** and **β**_{2} is perpendicular to **α**, then** β**₁ × **β**₂ is equal to:

**[2019]**

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

**Option B**: 3**i** – 9**j** – 5**k**

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

**Option D**: (1 / 2) ( 3**i** – 9**j** – 5**k **)

**Show/Hide Answer Key**

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

**JEE Main Vector Questions No: 89**

Let **a **= **i **+ **j **+ √2**k**, **b **= b₁**i** + b₂**j **+ √2**k** and** c **= 5**i **+ **j **+ √2**k** 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**: 4

**Show/Hide Answer Key**

**Option B: 6**

**JEE Mathematics Vector Questions No: 90**

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