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 Vectors Questions Answer Keys Solutions*.

### JEE Mains Mathematics Vectors Questions Bank

**JEE Main Vector Questions No: 121**

Let **a**, **b**, **c** be three vectors mutually perpendicular to each other and have same magnitude. If a vector **r** satisfies. **a **× { (**r **– **b**) × **a **} + **b × **{ (**r **– **c**) × **b **} + **c × **{ (**r **– **a**) × **c **} =**0, **then **r** is equal to

**[2021]**

**Option A**: (1/3) (**a **+ **b **+ **c**)

**Option B**: (1/3) (2**a **+ **b **– **c**)

**Option C**: (1/2) (**a **+ **b **+ **c**)

**Option D**: (1/2) (**a **+ **b **+ 2**c**)

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**Option C: (1/2) (a + b + c)**

**JEE Mains Math Vector Questions No: 122**

A line ‘l’ passing through origin is perpendicular to the line I_{1} : **r** = (3 + t)**i** + (1 + 2t)**j** + (4 + 2t)**k ,**I_{2} : **r **= (3 + 2s)**i** + (3 + 2s)**j** + (2 + s)**k.** If the co-ordinates of the point in the first octant on ‘l_{2}‘ at a distance of √17 from the point of intersection of ‘I’ and ‘I_{1}‘ are (a, b, c) then 18(a + b + c) is equal to

**[2021]**

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**Correct Ans: 44**

**JEE Main Math Vector Questions No: 123**

Let** a **= **i **+ a**j** + 3**k** and 3**i **– a**j **+ **k**. If the area of the parallelogram whose adjacent sides are represented by the vectors **a** and **b** is 8√3 square units, then** a ∙ b** is equal to

**[2021]**

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**Correct Ans: 2**

**JEE Vector Questions No:124**

Let **a **= **i **+ 2**j **– **k**, **b **= **i **– **j** and **c **= **i **– **j **– **k** be three given vectors, if **r** is a vector such that **r **× **a **= **c **× **a** and **r ∙ b **= 0, then **r ∙ a** is equal to

**[2021]**

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**Correct Ans: 12**

**JEE Main Vector Questions No: 125**

If **a** = α**i **+ β**j **+ 3**k, ****b **= -β**i **– α**j **– **k** and **c **= **i **– 2**j **– **k** such that **a · b **= 1 and **b · c **= −3, then (1/3) ((**a** × **b**) **∙ c**) is equal to

**[2021]**

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**Correct Ans: 2**

**JEE Mathematics Vector Questions No: 126**

In a triangle ABC, if | **BC **| = 8, | **CA **| = 7, | **AB **| = 10, then the projection of the vector | **AB **| on | **AC **| is equal to :

**[2021]**

**Option A**: (115 / 16)

**Option B**: (25 / 4)

**Option C**: (127 / 20)

**Option D**: (85 / 14)

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**Option D: (85 / 14)**

**JEE Mathematics Vector Questions No: 127**

If (**a **+ 3**b**) is perpendicular to (7**a **– 5**b**) and (**a **– 4**b**) is perpendicular to (7**a **– 2**b**), then the angle between **a** and **b** (in degrees) is

**[2021]**

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**Correct Ans: 60**

**Vector JEE Questions No: 128**

Let **a**=**i **+ **j **+ **k**, **b **and **c **= **j **– **k** be three vectors such that **a **× **b **= **c **and** a ∙ b **= 1. If the length of projection vector of the vector **b** on the vector **a **× **c** is l, then the value of 3l² is equal to

**[2021]**

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**Correct Ans: 2**

**Vector JEE Main Questions No: 129**

If the projection of the vector **i **+ 2**j **+ **k** on the sum of the two vectors 2**i **+ 4**j **– 5**k** and –????**i **+ 2**j **+ 3**k** is 1, then ???? is equal to

**[2021]**

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**Correct Ans: 5**

**JEE Main Math Vector Questions No: 130**

Let three vectors **a, b** and **c **be such that **c** is coplanar with **a** and **b**, **a ∙ ****c **= 7 and **b** is perpendicular to **c**, where **a **= – **i **+ **j **+ **k** and **b **= 2**i **+ **k**, then the value of 2 | **a **+ **b **+ **c **|^{2} is

**[2021]**

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**Correct Ans: 75**

**JEE Main Math Vector Questions No:131**

If vectors **a**_{1}_{ }= x**i **– **j **+ **k** and **a**_{2} = **i **+ y**j **+ z**k** are collinear, then a possible unit vector parallel to the vector x**i **+ y**j **+ z**k** is

**[2021]**

**Option A**: (1 / √3) (**i **– **j **+ **k**)

**Option B**: (1 / √3) (**i **+ **j** – **k**)

**Option C**: (1 / √2) (**i **– **j**)

**Option D**: (1 / √2) (-**j** + **k**)

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**Option A: (1 / √3) (i – j + k)**

**JEE Main Vector Questions No: 132**

Let the position vectors of two points P and Q be 3**i **– **j **+ 2**k** and **i **+ 2**j **– 4**k**, respectively. Let R and S be two points such that the direction ratios of lines PR and QS are (4, -1, 2) and (-2, 1, -2), respectively. Let lines PR and QS intersect at T. If the vector **TA** is perpendicular to both** PR** and **QS** and the length of vector **TA** is √5 units, then the modulus of a position vector of A is:

**[2021]**

**Option A**: √482

**Option B**: √227

**Option C**: √5

**Option D**: √171

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**Option D: √171**

**JEE Mathematics Vector Questions No: 133**

Let O be the origin. Let **OP **= x**i **+ y**j **– **k** and **OQ **= –**i **+ 2**j **+ 3x**k**, x, y ∈ R, x > 0, be such that | **PQ **|= √20 and the vector **OP** is perpendicular to** OQ**. If **OR **= 3**i **+ z**j **– 7**k**, z ∈ R, is coplanar with **OP** and **OQ**, then the value of x² + y^{2 }+ z² is equal to

**[2021]**

**Option A**: 7

**Option B**: 9

**Option C**: 2

**Option D**: 1

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**Option B: 9**

**JEE Mathematics Vector Questions No: 134**

For p > 0, a vector **V**_{2} = 2**i **+ (p + 1)**j** by obtained by rotating the vector **V**_{1} = √3p**i **+ **j** by an angle θ about origin in counter clockwise direction. If tan θ = (α√3 – 2) / (4√3 + 3)), then the value of α is equal to

**[2021]**

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**Correct Ans: 6**

**Vector JEE Questions No: 137**

Let **a**, **b**, **c** be three mutually perpendicular vectors of the same magnitude and equally inclined at an angle θ, with the vector **a **+ **b **+ **c**. Then 36cos^{2}2θ is equal is

**[2021]**

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**Correct Ans: 4**

**Vector JEE Main Questions No: 136**

Let a vector **a** be coplanar with vectors **b **= 2**i **+ **j **+ **k** and **c **= **i **– **j **+ **k**. If **a** is perpendicular to **d **= 3**i **+ 2**j **+ 6**k** and | **a **| = √10. Then a possible value of [**a b c**] + [**a b d**] + [**a c d**] is equal to :

**[2021]**

**Option A**: -42

**Option B**: -40

**Option C**: -29

**Option D**: -38

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**Option A: –42**

**JEE Main Math Vector Questions No: 137**

Let be two vectors. If **p **= 2**i **+ 3**j **+ **k** and **q **= **i **+ 2**j **+ **k** vector **r **= (α**i **+ β**j **+ γ**k**) is perpendicular to each of the vectors (**p **+ **q**) and (**p **– **q**), and | **r **| = √3, then | α | + | β | + | γ | is equal to

**[2021]**

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**Correct Ans: 3**

**JEE Main Math Vector Questions No: 138**

Let **a** and **b** be two vectors such that | 2**a** + 3**b **| = |3**a** + **b**| and the angle between **a** and **b** is 60°. If (1/8)**a** is a unit vector, | **b **| then is equal to :

**[2021]**

**Option A**: 4

**Option B**: 6

**Option C**: 5

**Option D**: 8

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**Option C: 5**

**JEE Main Math Vector Questions No: 139**

Let **a **= 2**i **– **j **+ 2**k** and **b **= **i **+ 2**j **– **k**. Let a vector **v** be in the plane containing **a** and **b**. If **v** is perpendicular to the vector 3**i **+ 2**j **– **k** and its projection on **a** is 19 units, then | 2**v |**² is equal to

**[2021]**

**Show/Hide Answer Key**

**Correct Ans: 1494**

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 | |