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 Mathematics Vectors Questions Answer Keys Solutions*.

### JEE Mains Mathematics Vectors Questions Bank

**JEE Mathematics Vector Questions No: 31**

If C is the mid point of AB and P is any outside AB, then

**[2005]**

**Option A**: **PA **+ **PB **= 2**PC**

**Option B**: **PA **+ **PB **= **PC**

**Option C**: **PA **+ **PB **+ 2**PC **= 0

**Option D**: **PA **+ **PB **+ **PC **= 0

**Show/Hide Answer Key**

**Option A: PA + PB = 2PC**

**JEE Main Math Vector Questions No: 32**

The value of a, for which the points A, B. C with position vectors 2**i **– **j** + **k**, **i **– 3**j** – 5**k**, and a**i **– 3**j** + **k**, respectively are the vertices of a right-angled triangle with C = (π/2) are

**[2006]**

**Option A**: 2 and 1

**Option B**: –2 and -1

**Option C**: –2 and 1

**Option D**: 2 and -1

**Show/Hide Answer Key**

**Option A: 2 and 1**

**Vector JEE Questions No: 33**

A particle has tow velocities of equal magnitude inclined to each other at an angle θ. If one of them is heated the angle between the other and the origin resultant velocity is bisected by the new resulted. Then θ is

**[2006]**

**Option A**: 90^{o}

**Option B**: 120^{o}

**Option C**: 40^{o}

**Option D**: 60^{o}

**Show/Hide Answer Key**

**Option B: 120 ^{o}**

**Vector JEE Main Questions No: 34**

If (**a ×** **b**) × **c **= **a ****× (b ****× c**) where **a , b, c ** are any three vectors such **ab **≠ 0 **bc **≠ 0 then ** a ** and **c ** are

**[2006]**

**Option A**: Inclined at an angle of (π/3) between them

**Option B**: Inclined at an angle of (π/6) between them

**Option C**: Perpendicular

**Option D**: Parallel

**Show/Hide Answer Key**

**Option D: Parallel**

**Vector Questions for JEE Mains Questions No: 35**

ABC is a triangle right angled at A. The resultant of the forces acting along AB, AC with magnitudes 1/AB and 1/AC respectively is the force along AD, where D is the foot of the perpendicular from A onto BC. The magnitude of the resultant is

**[2006]**

**Option A**: ( AB^{2} + AC^{2 }/ (AB^{2}) (AC^{2}) )

**Option B**: ( (AB) (AC) / AB + AC )

**Option C**: (1/AB) + (1/AC)

**Option D**: (1/AD)

**Show/Hide Answer Key**

**Option D: (1/AD)**

**Vector JEE Math Questions No: 36**

If **u ** and **v ** are unit and θ is the acute angle between them, then 2 θ > 3 θ is a unit vector for

**[2007]**

**Option A**: Exactly two values of θ

**Option B**: More than two values of θ

**Option C**: No value of θ

**Option D**: Exactly one values of θ

**Show/Hide Answer Key**

**Option D: Exactly one values of θ**

**JEE Vector Questions No:37**

Let **a **= **i** + **j** + **k **,** b** = **i **– **j **+ 2**k **and **c **= x**i **+ (x-2)**j **– **k.** If the vector **c** lies in the plane of **a **and **b** then x equals

**[2007]**

**Option A**: -4

**Option B**: -2

**Option C**: 0

**Option D**: 1

**Show/Hide Answer Key**

**Option B: -2**

**Vector for JEE Main Questions No: 38**

The non-zero vectors **a,** **b** and **c** are related by **a** = 8**b** and **c**= -7**b** . Then the angle between **a **and **c** is

**[2008]**

**Option A**:0

**Option B**: π/4

**Option C**: π/2

**Option D**: π

**Show/Hide Answer Key**

**Option D: π**

**JEE Mains Vector Questions No: 39**

The vector **a **= α**i **+ 2**j** + βk lies in the plane of the vectors **b** = **i** + **j** and **c** = **j**+ **k** and bisects the angle between **b** and** c** .Then which one of the following gives possible values of α and β?

**[2008]**

**Option A**: α = 2, β = 2

**Option B**: α = 1, β = 2

**Option C**: α = 2, β = 1

**Option D**: α = 1, β = 1

**Show/Hide Answer Key**

**Option D: α = 1, β = 1**

**JEE Mains Math Vector Questions No: 40**

If **u**, **v**, **w** are non-coplanar vectors and p, q are real numbers, then the equality [ 3**u** p**v** p**w **] – [ p**v** **w **q**u **] – [ 2**w** q**v ** q**u **] = 0 holds for

**[2009]**

**Option A**: Exactly one value of (p,q)

**Option B**: Exactly two value of (p,q)

**Option C**: More than two but not all values of (p,q)

**Option D**: All values of (p,q)

**Show/Hide Answer Key**

**Option A:****Exactly one value of (p,q)**

**Vector Questions for JEE Questions No: 41**

Let **a** = **j** – ** k** and **c** = **i** – j – ** k**. Then vector b satisfying **a** × **b** + **c** = **0** and **a** × **b **= 3 is

**[2010]**

**Option A**: 2**i** – j + 2**k**

**Option B**: **i** – j – 2**k**

**Option C**: **i** + j – 2**k**

**Option D**: –**i** + j – 2**k**

**Show/Hide Answer Key**

**Option D: –i + j – 2k**

**JEE Vector Questions No:42**

If the vectors **a **= **i **– **j **+ 2**k**, **b** = 2**i** + 4**j** + **k** and **c** = ????**i** +** j** +μ ֝**k** are mutually orthogonal, then (????, μ) =

**[2010]**

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

**Option B**: (-2,3)

**Option C**: (3,-2)

**Option D**: (-3,2)

**Show/Hide Answer Key**

**Option D: (-3,2) **

**JEE Mathematics Vector Questions No: 43**

If the vectors ā = **i** – **b** + 2**k**, **b **= 2**i** + 4**j** + **k** and **c **= ????**i **+ **j **+ μ**k** are mutually orthogonal, then (????,μ) =

**[2010]**

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

**Option B**: (-2, 3)

**Option C**: (3, -2)

**Option D**: (-3, 2)

**Show/Hide Answer Key**

**Option D: (-3, 2)**

**JEE Main Vector Questions No: 44**

Let **a**, **b**, **c** be three non-zero vectors which are pairwise non-collinear. If **a** +3**b** is collinear with **c** and **b** + 2**c** is collinear with **a** , then **a** + 3**b** + **6c** is

**[2011]**

**Option A**: **0**

**Option B**: **a **+ **c**

**Option C**: **a**

**Option D**: **c**

**Show/Hide Answer Key**

**Option A: 0**

**JEE Mathematics Vector Questions No: 45**

If the vectors p**i** + **j** + **k**, **i** + q**j** + **k** and **i** +** j** + r**k** (p ≠ q ≠ r ≠ 1) are coplanar, then the value of pqr – (p + q + r) is

**[2011]**

**Option A**: -1

**Option B**: -2

**Option C**: 2

**Option D**: 0

**Show/Hide Answer Key**

**Option B: -2**

**JEE Main Vector Questions No: 46**

If **a **= (1/√10) (3**i **+ **k**) and **b **= (1/7) (2**i **+ 3**j **– 6**k**), then the value of (2**a **– 2**b**) [ (**a **x **b**) x (**a **+ 2**b**) ] is

**[2011]**

**Option A**: -3

**Option B**: 5

**Option C**: 3

**Option D**: -5

**Show/Hide Answer Key**

**Option D: -5**

**JEE Mathematics Vector Questions No: 47**

The vectors **a ** and **b ** are not perpendicular and **c ** and **d ** are two vectors satisfying **b** x **c** = ** b** x **d** and ** a** ∙** d **= 0. Then the vector **d ** is equal to

**[2011]**

**Option A :**

**Option B**:

**Option C**:

**Option D**:

**Show/Hide Answer Key**

**Option C: C**

**JEE Main Math Vector Questions No: 48**

Let ABCD be a parallelogram such that** AB** = **q**, **AD** = **p** and ∠BAD be an acute angle. If **r** is the vector that coincides with the altitude directed from the vertex B to the side AD, then **r **is

**[2012]**

**Option A**: **r ** = **q **– [( **p** ∙ **q** )/( **p** ∙** p** )] **p**

**Option B**: **r ** = -3**q **+ [3 (**p** ∙** q) **/ (**p** ∙** p**)] **p**

**Option C**: **r ** = 3**q **– [3(**p** ∙** q )**/(**p **∙** p**)] **p**

**Option D**: **r ** = –**q **+ [(**p** ∙** q) **/ (**p** ∙** p**)] **p**

**Show/Hide Answer Key**

**Option D: r = -q + [(p ∙ q / p** **∙ p)] p**

**Vector JEE Questions No: 49**

Let **a** and **b** be two unit vectors. If the vectors **c** = **a **+ 2**b** and **d **= 5**a** – 4**b** are perpendicular to each other, then the angle between **a** and **b** is

**[2012]**

**Option A**: π/3

**Option B**: π/4

**Option C**: π/6

**Option D**: π/2

**Show/Hide Answer Key**

**Option A: π/3**

**JEE Main Math Vector Questions No: 50**

If **a **= **i **– 2**j **+ 3**k,** **b **= 2**i **+ 3**j **– **k ** and **c **= ????**i **+ **j **+ (2???? – 1)** ****k **are coplanar vectors , then ???? is equal to

**[2012]**

**Option A**: 0

**Option B**: -1

**Option C**: 2

**Option D**: 1

**Show/Hide Answer Key**

**Option A: 0**

**JEE Mains Vector Questions No: 51**

If **a **= **i **– 2**j **+ 3**k**, **b **= 2**î **+ 3**j **– **k** and **c **= r**i **+ **j **+ (2r – 1)**k** are three vectors such that **c **is parallel to the plane of** a** and **b**, then r is equal to

**[2012]**

**Option A**: 1

**Option B**: -1

**Option C**: 0

**Option D**: 2

**Show/Hide Answer Key**

**Option C: 0**

**Vector JEE Questions No: 52**

Statement I : If the points (1, 2, 2) (2, 1, 2) (2, 2, z) (1, 1, 1) are coplanar, then z=2

Statement II: If the 4 points P, Q, R and S are coplanar, then the volume of the tetrahedron PQRS is 0

**[2012]**

**Option A**: Statement I is false Statement II is true

**Option B**: Statement I is true Statement II is false

**Option C**: Statement I is true Statement II is true, Statement II is a correct explanation of Statement I

**Option D**: Statement I is false Statement II is true, Statement II is not a correct explanation of Statement I

**Show/Hide Answer Key**

**Option A: Statement I is false Statement II is true**

**Vector JEE Main Questions No: 53**

If **u **= **j **+ 4**k, v = i +** 3**k **and **w** = cosθ **i **+ sinθ **j **are vectors in 3 dimensional space, then the maximum value of |**u **×** v **∙** w**| is

**[2012]**

**Option A**: √3

**Option B**: 5

**Option C**: √14

**Option D**: 7

**Show/Hide Answer Key**

**Option B: 5**

**Vector Questions for JEE Mains Questions No: 54**

Statement I : The vectors **a**, **b **and **c **lie in the same plane if and only if **a** **∙** ( **b** ×** c **)= 0

Statement II : The vectors **u **and **v **are perpendicular if and only if **u ∙** **v **= 0 where **u **× **v **is a perpendicular to the plane of **u ** and **v**

**[2012]**

**Option A**: Statement I is false Statement II is true

**Option B**: Statement I is true Statement II is true, Statement II is a correct explanation for Statement I

**Option C**: Statement I is true Statement II is false

**Option D**: Statement I is true Statement II is true, Statement II is not a correct explanation for Statement I

**Show/Hide Answer Key**

**Option C: Statement I is true Statement II is false**

**Vector JEE Questions No: 55**

ABCD is parallelogram. The position vectors of A and C are respectively, 3**i** + 3**j** + 5**k** and** i **– 5**j **– 5**k**. If M is the midpoint of the diagonal DB, then the magnitude of the projection of **OM** on **OC**, where O is the origin, is

**[2012]**

**Option A**: 7√51

**Option B**: (7 / √50)

**Option C**: 7√50

**Option D**: (7 / √51)

**Show/Hide Answer Key**

**Option D: (7 / √51)**

**Vector JEE Main Questions No: 56**

A unit vector which is perpendicular to the vector 2**i **– **j **+ 2**k** and is coplanar with the vectors **i **+ **j** – **k** and 2**i** + 2**j **– **k** is

**[2012]**

**Option A**: (2**j **+ **k**) / √5

**Option B**: (3**i **+ 2**j – **2**k** ) / √17

**Option C**: (3**i** + 2**j** + 2**k**) / √17

**Option D**: (2**i** + 2**j – **2**k) **/ 3

**Show/Hide Answer Key**

**Option D: (2i + 2 j − 2k ) / 3**

**Vector Questions for JEE Mains Questions No: 57**

If **a** + **b** + **c** = 0, | **a **| = 3, | **b **| = 5, and | **c **| = 7, then the angle between **a ** and **b ** is

**[2012]**

**Option A**: π/3

**Option B**: π/4

**Option C**: π/6

**Option D**: π/2

**Show/Hide Answer Key**

**Option A: π/3**

**Vector JEE Main Questions No: 58**

If the vectors **AB** = 3**i** + 4**k** and **AC** = 5**i** – 2**j** + 4**k** are the sides of a triangle ABC, then the length of the median through A is

**[2013]**

**Option A**: √72

**Option B**: √33

**Option C**: √45

**Option D**: √18

**Show/Hide Answer Key**

**Option B: √33**

**Vector Questions No: 59**

The vector (**i** × **a ∙ b**) **i **+ (**j** × **a ∙ b**)** j **+ (**k** × **a ∙ b**) **k ** is equal to

**[2013]**

**Option A**: **b ****× a**

**Option B**: **a**

**Option C**: **a **× **b **

**Option D**: **b **

**Show/Hide Answer Key**

**Option C: a × b **

**Vector Questions No: 60**

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

**[2013]**

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

**Option B**: (3√3 / 2)

**Option C**: 3

**Option D**: (3 / 2)

**Show/Hide Answer Key**

**Option D: (3 / 2)**

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 | |