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 Math Vectors Questions Answer Keys Solutions*.

### JEE Mains Mathematics Vectors Questions Bank

**JEE Vector Questions No:91**

Let **α **= (λ – 2) **a **+ **b **and **β **= (4λ – 2) **a** + 3**b** be two given vectors where vectors **a** and **b** are non-collinear. The value of λ for which vectors **α** and **β** are collinear, is

**[2019]**

**Option A**: -4

**Option B**: -3

**Option C**: 4

**Option D**: 3

**Show/Hide Answer Key**

**Option A: -4**

**JEE Main Vector Questions No: 92**

Let √3**i **+ **j**, **i **+ √3**j** and β**i **+ (1 – β)**j** respectively be the position vectors of the points A, B and C with respect to the origin O. If the distance of C from the bisector of the acute angle between OA and OB is 3 / √2 then the sum of all possible values of β is :

**[2019]**

**Option A**: 4

**Option B**: 3

**Option C**: 2

**Option D**: 1

**Show/Hide Answer Key**

**Option D: 1**

**JEE Mathematics Vector Questions No: 93**

Let **a **= **i **+ 2**j **+ 4**k**, **b **= **i **+ ????**j **+ 4**k** and** c **= 2î + 4**j **+ (????² − 1)**k** be coplanar vectors. Then the non-zero vector **a **× **c** is

**[2019]**

**Option A**: -10**i **– 5**j**

**Option B**: -14**i **– 5**j**

**Option C**: -14**i **+ 5**j**

**Option D**: -10**i **+ 5**j**

**Show/Hide Answer Key**

**Option D: -10i + 5j**

**JEE Mathematics Vector Questions No: 94**

The sum of the distinct real values of μ, for which the vectors, µ**i **+ **j **+ **k**, **i **+ µ**j **+ **k**,** i **+ **j **+ µ**k**, are co-planar is

**[2019]**

**Option A**: -1

**Option B**: 0

**Option C**: 1

**Option D**: 2

**Show/Hide Answer Key**

**Option A: -1**

**Vector JEE Questions No: 95**

If a unit vector **a** makes angles π/3 with **i, **(n/4) with **j **and θ ∈ (0, π) with** k**, then a value of θ, is:

**[2019]**

**Option A**: (5π / 6)

**Option B**: (π / 4)

**Option C**: (5π / 12)

**Option D**: (2π / 3)

**Show/Hide Answer Key**

**Option D: (2π / 3)**

**Vector JEE Main Questions No: 96**

Let α ∈ R and the three vectors **a **= α**i **+ **j **+ 3**k**, **b **= 2**i **+ **j **– α**k** and **c **= α**î **– 2**j **+ 3**k**. Then the set S = (α: **a, b** and **c** are coplanar)

**[2019]**

**Option A**: is singleton

**Option B**: is empty

**Option C**: contains exactly two positive numbers

**Option D**: contains exactly two numbers only one of which is positive

**Show/Hide Answer Key**

**Option B: is empty**

**JEE Main Math Vector Questions No: 97**

If the volume of parallelopiped formed by the vectors **i **+ λ**j **+ **k**, **j **+ λ**k** and λ**i **+ **k** is minimum, then λ is equal to:

**[2019]**

**Option A**: (-1 / √3)

**Option B**: (1 / √3)

**Option C**: √3

**Option D**: -√3

**Show/Hide Answer Key**

**Option B: (1 / √3)**

**JEE Main Math Vector Questions No: 98**

Let **a **= 3**i **+ 2**j **+ 2**k** and **b **= **i **+ 2**j **– 2**k** be two vectors. If a vector perpendicular to both the vectors **a **+ **b** and **a **– **b** has the magnitude 12 then one such vector is

**[2019]**

**Option A**: 4(2**i **+ 2**j **+ 2**k**)

**Option B**: 4(2**i **– 2**j **– **k**)

**Option C**: 4(2**i **+ 2**j **– **k**)

**Option D**: 4(-2**i** – 2**j **+ **k**)

**Show/Hide Answer Key**

**Option B: 4(2i – 2j – k)**

**JEE Main Vector Questions No: 99**

Let **a** = **i **– 2**j **+ **k** and **b **= **i **– **j **+ **k** be two vectors. If **c** is a vector such that **b **× **c** = **b **× **a** and **c ∙ a** = 0, then **c ∙ b** is equal to:

**[2020]**

**Option A**: (-3 / 2)

**Option B**: (1 / 2)

**Option C**: (-1 / 2)

**Option D**: -1

**Show/Hide Answer Key**

**Option C: (-1 / 2)**

**JEE Mathematics Vector Questions No: 100**

Let **a**, **b** and **c** be three vectors such that | **a **| = √3, | **b **| = 5, **b ∙ c** = 10 and the angle between **b **and **c **is (π/3). If** b** is perpendicular to the vector **b** × **c ** then | **a** × (**b** × **c**) is equal to

**[2020]**

**Show/Hide Answer Key**

**Correct Ans: 30**

**JEE Main Math Vector Questions No: 101**

If **a** = 2**i **+ 3**j **+ 2**k,** then the value of | **i** × (**a ×** **i**) |² + | **j** × (**a ×** **j**) **|**² + | **k ×** (**a × ****k**) |² is equal to

**[2020]**

**Show/Hide Answer Key**

**Correct Ans: 18**

**Vector JEE Questions No: 102**

Let x_{0}, be the point of local maxima of f(x) = **a ∙** (**b × ****c**), where **a **= x**i **– 2**j **+ 3**k**, **b **= -2**i **+ x**j **– **k** and **c **= 7î – 2**j **+ x**k**. Then the value of** a ∙ b **+ **b ∙ c** + **c ∙ a** at x = x_{0} is:

**[2020]**

**Option A**: -4

**Option B**: -30

**Option C**: 14

**Option D**: -22

**Show/Hide Answer Key**

**Option D: -22**

**Vector JEE Main Questions No: 103**

If the volume of a parallelepiped, whose coterminous edges are given by the vectors **a **= **i **+ **j **+ n**k**, **b **= 2**i **+ 4**j **– n**k** and **c **= **i **+ n**j **+ 3**k **(n ≥ 0), is 158 cu. units, then:

**[2020]**

**Option A**: **a ∙ c **= 17

**Option B**: **b ∙ c **= 10

**Option C**: n = 7

**Option D**: n = 9

**Show/Hide Answer Key**

**Option B: b ∙ c = 10**

**JEE Mathematics Vector Questions No: 104**

A vector **a** = α**i** + 2**j** + β**k** (α, β ∈ R) lies in the plane of the vectors, **b **= **i **+ **j** and **c **= **i **– **j** + 4**k**. If **a** bisects the angle between **b** and **c**, then:

**[2020]**

**Option A**: **a **∙** i **+ 3 = 0

**Option B**: **a **∙ **i **+ 1 = 0

**Option C**: **a **∙** k **+ 2 = 0

**Option D**: **a **∙** k **+ 4 = 0

**Show/Hide Answer Key**

**Option C: a ∙ k + 2 = 0**

**Vector JEE Questions No: 105**

Let the volume of a parallelepiped whose coterminous edges are given by **u **= **i **+ **j **+ ????**k**, **v **= **i **+ **j **+ 3**k** and **w **= 2**i **+ **j **+ **k** be 1 cu. unit. If θ be the angle between the edges **ū** and **w**, then cosθ can be:

**[2020]**

**Option A**: (7 / 6√6)

**Option B**: (7 / 6√3)

**Option C**: (5 / 7)

**Option D**: (5 / 3√3)

**Show/Hide Answer Key**

**Option B: (7 / 6√3)**

**Vector JEE Main Questions No: 106**

The projection of the line segment joining the points (1, -1, 3) and (2, -4, 11) on the line joining the points (-1, 2, 3) and (3, -2, 10) is

**[2020]**

**Show/Hide Answer Key**

**Correct Ans: 8**

**JEE Main Math Vector Questions No: 107**

Let **a, b** and **c** be three unit vectors such that | **a **− **b **|² +| **ā** − **c **|² = 8. Then | **ā** + 2**b **|² + | **ā** + 2**c **|² is equal to

**[2020]**

**Show/Hide Answer Key**

**Correct Ans: 2**

**JEE Main Math Vector Questions No: 108**

Let the vectors **a**, **b**, **c** be such that | **ā** | = 2, | **b **| = 4 and | **c **| = 4. If the projection of **b **on **a** is equal to the projection of **c** on **a** and **b** is perpendicular to **c**, then the value of | **a **+ **b **– **c **| is

**[2020]**

**Show/Hide Answer Key**

**Correct Ans: 6**

**JEE Main Math Vector Questions No: 109**

If **x** and **y **be two non-zero vectors such that | **x **+ **y **| = | **x** | and 2**x **+ ????**y** is perpendicular to **y**, then the value of ???? is

**[2020]**

**Show/Hide Answer Key**

**Correct Ans: 1**

**JEE Mains Vector Questions No: 110**

If **a** and **b** are unit vectors, then the greatest value of √3 | **a **+ **b **| + | **a **– **b **| is

**[2020] **

**Show/Hide Answer Key**

**Correct Ans: 4**

**JEE Main Math Vector Questions No: 111**

If the vectors, **p **= (a + 1)**i** + a**j **+ a**k**, **q **= a**i **+ (a + 1)**j** +a**k** and **r **= a**i **+ a**j **+ (a + 1)**k** (a ∈ R) are coplanar and 3 (**p ∙ q**)² – λ | **r × ****q **|² = 0, then the value of λ is

**[2020]**

**Show/Hide Answer Key**

**Correct Ans: 1**

**JEE Main Math Vector Questions No: 112**

Let the position vectors of points ‘A’ and ‘B’ be **i **+ **j **+ **k** and 2**i **+ **j **+ 3**k**, respectively. A point ‘P’ divides the line segment AB internally in the ratio λ : 1 (λ > 0). If O is the region and **OB** ×** OP **– 3 | **OA **× **OP **|^{2 }= 6, then λ is equal to

**[2020]**

**Show/Hide Answer Key**

**Correct Ans: 0.8**

**JEE Mains Math Vector Questions No: 113**

Let a, b, c ∈ R be such that a² + b² + c² = 1. If acosθ – bcos(θ + 2π/3) = c cos(θ + 4π/3) where θ = (π/9), then the angle between the vectors a**i **+ b**j **+ c**k** and b**i** + c**j **+ a**k** is

**[2020]**

**Option A**: (π / 2)

**Option B**: (2π / 3)

**Option C**: (π / 9)

**Option D**: 0

**Show/Hide Answer Key**

**Option A: (π / 2)**

**JEE Main Math Vector Questions No: 114**

If **a** and **b** are perpendicular, then **a **× (**a **× (**a **× (**a **× **b**) ) ) is equal to :

**[2021]**

**Option A**: **a** × **b**

**Option B**: **0**

**Option C**: (1/2) | **a **|^{4 }**b**

**Option D**: | **a **|^{4 }**b**

**Show/Hide Answer Key**

**Option D: | a | ^{4 }b**

**JEE Main Math Vector Questions No: 115**

Let** c** be a vector perpendicular to the vectors **a **= **i **+ **j **– **k** and **b **= **i **+ 2**j **+ **k**. If **c ∙ **(**i **+ **j **+ 3**k**) = 8 then the value of **c ∙ **(**a ×** **b**) is equal to

**[2021]**

**Show/Hide Answer Key**

**Correct Ans: 28**

**JEE Main Math Vector Questions No: 116**

Let** a **= **i **+ 2**j **– 3**k** and **b **= 2**i **– 3**j **+ 5**k**. If **r × ****a **= **b × ****r**, **r ∙ **(a**i **+ 2**j **+ **k**) = 3 and** r ∙ **(2**i **+ 5**j **– α**k**) = 1 α ∈ R, then the value of α +| **r **|^{2} is equal to:

**[2021]**

**Option A**: 15

**Option B**: 13

**Option C**: 9

**Option D**: 11

**Show/Hide Answer Key**

**Option A: 15**

**JEE Main Math Vector Questions No: 117**

Let **a** = 2**i **– 3**j **+ 4**k** and **b **= 7**i **+ **j **– 6**k.** If **r** × **a **= **b** × **r**, **r** **∙** (**i** + 2**j**+ **k**) = −3, then **r** **∙** (2**i **– 3**j** + **k**)

**[2021]**

**Option A**: 10

**Option B**: 13

**Option C**: 8

**Option D**: 12

**Show/Hide Answer Key**

**Option D: 12**

**JEE Mains Math Vector Questions No: 118**

Let **a **= **i **– α**j **+ β**k**, **b **= 3**i **+ β**j **– α**k** and **c **= – α**i **– 2**j **+ **k**, where α and β are integers. If **a ∙ b **= -1 and **b ∙ c **= 10, then (**a **× **b**) **∙** **c** is equal to

**[2021]**

**Show/Hide Answer Key**

**Correct Ans: 9**

**JEE Main Math Vector Questions No: 119**

Let **a **= **i **+ **j **+ **k** and **b **= **j **– **k.** If **c** is a vector such that **a × ****c **= **b** and **a ∙ c** = 3, then **a ∙** (**b **× **c**) is equal to

**[2021]**

**Option A**: -2

**Option B**: -6

**Option C**: 6

**Option D**: 2

**Show/Hide Answer Key**

**Option A: -2**

**JEE Vector Questions No:120**

Let **a **= **i **+ 5**j **+ α**k**, **b **= **i **+ 3**j **+ β**k** and **c **= −**i** + 2**j **– 3**k** be three vectors such that, | **b **× **c **| = 5√3 and **a** is perpendicular to **b**. Then the greatest amongst the values of | **a** |² is

**[2021]**

**Show/Hide Answer Key**

**Correct Ans: 90**

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 | |