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 Previous Year Paper Vectors Questions Answer Keys Solutions*.

### JEE Mains Mathematics Vectors Questions Bank

**JEE Vector Questions No:1**

If **a** ×** b** = **b** ×** c** = **c** × **a** , then **a** + **b** + **c** is equal to

**[2002]**

**Option A**: abc

**Option B**: -1

**Option C**: 0

**Option D**: 2

**Show/Hide Answer Key**

**Option C : 0**

**JEE Main Vector Questions No: 2**

Let** a** = 3**i** – 5**j** and** b** = 6**i** + 3**j** are two vectors and **c** is a vector such that **c** = **a** × **b** , then | **a** | : | **b** | : | **c** | is equal to

**[2002]**

**Option A**: √34 : √45 : √39

**Option B**: √34 : √45 : 39

**Option C**: 34 : 39 : 45

**Option D**: 34 : 35 : 34

**Show/Hide Answer Key**

**Option B : √34 : √45 : 39**

**JEE Mathematics Vector Questions No: 3**

3λ**c** + 2μ(**a** × **b**) = 0, then

**[2002]**

**Option A**: 3λ + 2μ = 0

**Option B**: 3λ = 2μ

**Option C**: λ = μ

**Option D**: λ + μ = 0

**Show/Hide Answer Key**

**Option B: 3λ = 2μ**

**JEE Main Math Vector Questions No: 4**

If | **a** | = 5, | **b** | = 4, | **c** | = 3 thus what will be the value of | **a** ∙ **b** + **b** ∙ **c** + **c** ∙ **a **|. Given that **a** +** b** + **c **= 0

**[2002]**

**Option A**: 25

**Option B**: 50

**Option C**: -25

**Option D**: -30

**Show/Hide Answer Key**

**Option A: 25**

**Vector JEE Questions No: 5**

If **a**,** b**, **c** are vectors Show that** a** + **b** +**c** = 0 and | **a** | = 7, | **b** | = 5, I **c** | = 3, then the angle between vector **b** and **c** is

**[2002]**

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

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

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

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

**Show/Hide Answer Key**

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

**Vector JEE Main Questions No: 6**

If **a**, **b**, **c** are vectors such that [**a **∙ **b** ∙ **c**] = 4, then [ **a **×** b b **×** c c **×** a** ] is equal to

**[2002]**

**Option A**: 16

**Option B**: 64

**Option C**: 4

**Option D**: 8

**Show/Hide Answer Key**

**Option B: 64**

**Vector for JEE Mains Questions No: 7**

If | **a **| = 4, | **b** | = 2 and the angle between **a** and **b** is (π/6) then (**a** × **b**)^{2} is equal to

**[2002]**

**Option A**: 48

**Option B**:16

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

**Option D**: None of These

**Show/Hide Answer Key**

**Option B: 16**

**Vector Questions for JEE Questions No: 8**

If the vectors **c**, â = x**i**+ y**j** + z**k** and **b** =** j** are such that **a, c** and **b** form a right handed system then **c **is

**[2002]**

**Option A**: z**i **– x**k**

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

**Option C**: y**j**

**Option D**: –z**i **+ x**k**

**Show/Hide Answer Key**

**Option A: zi – xk**

**JEE Vector Questions No: 9**

Let **a, b** and **c** be three unit vectors such that **a **+ **b **+ **c **= **0**, if λ = **a ∙ b **+ **b ∙ c **+ **c ∙ a** and **d **= **a **× **b **+ **b **x **c **+ **c **× **a**, then the ordered pair, (λ,d) is equal to:

**[2002]**

**Option A**: (3/2, 3**a** × **c **)

**Option B**: (-3/2, 3**c** × **b**)

**Option C**: (3/2, 3**b** × **c **)

**Option D**: (-3/2, 3**a** × **b **)

**Show/Hide Answer Key**

**Option D: (-3/2, 3a × b )**

**JEE Mathematics Vector Questions No: 10**

If **a**,** b**, **c** are vectors such that **a **+ **b **+ **c **= 0 and | **a **| = 7 | **b **| = 5, | **c **| = 3 then angle between vector **b** and **c** is

**[2002]**

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

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

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

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

**Show/Hide Answer Key**

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

**Vector for JEE Questions No: 11**

Let **u** =** i** +** j**, **v** = **i** – **j** and **w** = **i** + 2**j** + 3**k** . If ñ is unit vector such that **u **× **n** = 0 and **v **× **n **= 0, then I **w** ∙ n I is equal to

**[2003]**

**Option A**: 0

**Option B:** 1

**Option C**: 2

**Option D**: 3

**Show/Hide Answer Key**

**Option D: 3**

**JEE Main Math Vector Questions No: 12**

A particle acted on by constant forces 4**i** + **j** – 3**k** and 3**i** + **j** – **k** is displaced from the point **i** + 2**j** + 3**k** to the point 5**i** + 4**j** +**k** . The total work done by the forces is

**[2003]**

**Option A**: 20 units

**Option B**: 30 units

**Option C**: 40 units

**Option D**: 50 units

**Show/Hide Answer Key**

**Option C: 40 units**

**JEE Mains Vector Questions No: 13**

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

**[2003]**

**Option A**: √18

**Option B**: √72

**Option C**: √33

**Option D**: √288

**Show/Hide Answer Key**

**Option C: √33**

**JEE Mains Math Vector Questions No: 14**

Consider points A, B, C and D with position vectors 7**i** – 4**j** + 7**k**,** i** – 6**j** + 10**k** , –**i** – 3j + 4**k **and 5**i** – **j** + 5**k** respectively. Then ABCD is a

**[2003]**

**Option A**: Square

**Option B**: Rhombus

**Option C**: Rectangle

**Option D**: None of these

**Show/Hide Answer Key**

**Option D: None of These**

**Vector Questions for JEE Questions No: 15**

If **u**, **v** and **w** are three non-coplanar vectors, then (**u** + **v** – **w**) ∙ (**u** – **v**) × (**v** – **w**) equals

**[2003]**

**Option A**: 0

**Option B**: **u** ∙ **v** × **w**

**Option C**: **u** ∙ **w** × **v**

**Option D**:** **3 **u** ∙ **v** × **w**

**Show/Hide Answer Key**

**Option B: u × v × w**

**JEE Vector Questions No:16**

**a**,** b,** **c** are 3 vectors, such that **a** + **b** + **c** = 0, | **a** | = 1, | **b** |= 2, | **c** I = 3. then **a** ∙** b** + **b** ∙** c **+ **c** ∙** a **is equal to

**[2003]**

**Option A**: 0

**Option B**: -7

**Option C**: 7

**Option D**: 1

**Show/Hide Answer Key**

**Option B: -7**

**JEE Main Vector Questions No: 17**

A tetrahedron has vertices at O (0, 0, 0), A (1, 2, 1), B (2, 1, 3) and C (-1, 1, 2). Then the angle between the faces OAB and ABC will be

**[2003]**

**Option A**: cos^{-1 }(19/35)

**Option B**: cos^{-1 }(17/31)

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

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

**Show/Hide Answer Key**

**Option A: cos ^{-1 }(19/35)**

**Vector Questions for JEE Mains Questions No: 18**

If

and vectors (1, a, a²), (1, b, b²) and (1, c, c²) are non-coplanar, then the product abc equals

**[2003]**

**Option A**: 0

**Option B**: 2

**Option C**: -1

**Option D**: 1

**Show/Hide Answer Key**

**Option C: -1**

**JEE Mathematics Vector Questions No: 19**

A particle moves towards east from a point A to a point B at the rate of 4 km/h and then towards north from B to C at the rate of 5 km/h. If AB = 12 km and BC = 5 km, then its average speed for its journey from A to C and resultant average velocity direct from A to C are respectively

**[2004]**

**Option A**: (17/4) km/h and (13/4) km/h

**Option B**: (13/4) km/h and (17/4) km/h

**Option C**: (17/9) km/h and (13/9) km/h

**Option D**: (13/9) km/h and (17/9) km/h

**Show/Hide Answer Key**

**Option A: 17/4 km/h and 13/4 km/h**

**JEE Main Math Vector Questions No: 20**

In a right angle ∆ABC, A = ∠90° and sides a, b, c are respectively, 5 cm, 4 cm and 3 cm. If a force F has moments 0, 9 and 16 in N cm. units respectively about vertices A, B and C, then magnitude of F is

**[2004]**

**Option A**: 3

**Option B**: 4

**Option C**: 5

**Option D**: 9

**Show/Hide Answer Key**

**Option C: 5**

**Vector JEE Questions No: 21**

Let **a**, **b** and **c** be non-zero vectors such that (**a** × **b**) × **c** = (1/3) | **b **| | **c **| | **a |** . If θ is the acute angle between the vectors **b** and **c**, then sin θ equals

**[2004]**

**Option A**: 1/3

**Option B**: √2/3

**Option C**: 2/3

**Option D**: 2√2/3

**Show/Hide Answer Key**

**Option D: 2√2/3**

**Vector JEE Main Questions No: 22**

Let **u**, **v**, **w** be such that | **u **| = 1, | **v **| = 2, | **w **| = 3. If the projection **v** along **u** is equal to that of **w** along **u** and **v**, **w** are perpendicular to each other then | **u** – **v** + **w **| equals

**[2004]**

**Option A**: 2

**Option B**: √7

**Option C**: √14

**Option D**: 14

**Show/Hide Answer Key**

**Option C: √14**

**Vector Questions for JEE Mains Questions No: 23**

If **a,** **b**, **c** are non-coplanar vectors and ???? is a real number, then the vectors **a** + 2**b** + **3c,** ????**b** + 4**c **and (2???? -1) **c** are non-coplanar for

**[2004]**

**Option A**: All values of ????

**Option B**: All except two values of ????

**Option C**: All except one value of ????

**Option D**: No value of ????

**Show/Hide Answer Key**

**Option C: All except one value of ????**

**Vector JEE Main Math Questions No: 24**

A particle is acted upon by constant forces 4**i** + **j** -3**k** and 3**i** +** j** – **k** which displace it from a point **i** + 2**j** + 3**k** to the point 5**i** + 4**j** + **k** . The work done in standard units by the forces is given by

**[2004]**

**Option A**: 40

**Option B**: 30

**Option C**: 25

**Option D**: 15

**Show/Hide Answer Key**

**Option A: 40**

**Vector JEE Main Math Questions No: 25**

Let **a**, **b** and **c** be three non-zero vectors such that no two of these are collinear. If the vector a 2b is collinear with **c** and **b** + 3**c** is collinear with **a** (???? being some non-zero scalar) then **a** + 2**b** + 6**c** equals

**[2005]**

**Option A**: ????**a**

**Option B**: ????**b**

**Option C**: ????**c **

**Option D**: 0

**Show/Hide Answer Key**

**Option D: 0**

**JEE Mains Vector Questions No: 26**

Let **a** = **i **–** k** , b= x**i** +** j** + (1 – x)**k** and **c** = y**i** + x**j** + (1 + x – y)**k** . Then [ **a**, **b**, **c** ]depends on

**[2005]**

**Option A**: Only y

**Option B**: Only x

**Option C**: Both x and y

**Option D**: Neither x and y

**Show/Hide Answer Key**

**Option D: Neither x and y**

**JEE Mains Math Vector Questions No: 27**

If a, b, c are non coplanar vectors and ???? is a real number then [ ???? ( **a** +** b **) ????^{2 }**b **????** c **] = [ **a b **+ **c b **] for

**[2005]**

**Option A**: Exactly one value of ????

**Option B**: No value of ????

**Option C**: Exactly three value of ????

**Option D**: Exactly two value of ????

**Show/Hide Answer Key**

**Option B: No value of ????**

**Vector Questions for JEE Questions No: 28**

Let a, b and c be distinct non negative numbers. If the vector a**i **+a**j **+ Ӄ, **i** +** k **and c**i** + c**j** + b**k** lie in a plane then c is

**[2005]**

**Option A**: The Geometric Mean of a and b

**Option B**: The Arithmetic Mean of a and b

**Option C**: Equal to Zero

**Option D**: The Harmonic Mean of a and b

**Show/Hide Answer Key**

**Option A: The Geometric Mean of a and b**

**JEE Vector Questions No:29**

For any vector **a **the value of ( **a **× **i **)^{2 }+ ( **a **× **j **)^{2 }+ ( **a **× **k **)^{2 }is equal to

**[2005]**

**Option A**: 3**a**^{2 }

**Option B**: **a**^{2 }

**Option C**: 2**a**^{2 }

**Option D**: 4**a**^{2 }

**Show/Hide Answer Key**

**Option C: 2a ^{2 }**

**JEE Main Vector Questions No: 30**

The distance between the line **r** = 2**i** – 2**j** + 3**k **+ ???? ( **i** – **j** + 4**k )** and the plane **r** ( **i** + 5**j** + **k **) = 5 is

**[2005]**

**Option A**: ( 10/9 )

**Option B**: ( 10/3√3 )

**Option C**: ( 3/10 )

**Option D**: ( 10/3 )

**Show/Hide Answer Key**

**Option B:( 10/3√3 )**

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 | |