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# JEE Main Math Previous Year Papers Vectors Questions Answer Keys Solutions

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



Option A: abc

Option B:  -1

Option C: 0

Option D: 2

Option C : 0

JEE Main Vector Questions No: 2

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



Option A: √34 : √45 : √39

Option B: √34 : √45 : 39

Option C: 34 : 39 : 45

Option D: 34 : 35 : 34

Option B : √34 : √45 : 39

JEE Mathematics Vector Questions No: 3

c + 2μ(a × b) = 0, then



Option A: 3λ + 2μ = 0

Option B: 3λ = 2μ

Option C: λ = μ

Option D: λ + μ = 0

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 + bc + ca |. Given that a + b + c = 0



Option A: 25

Option B: 50

Option C: -25

Option D: -30

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



Option A: 600

Option B: 300

Option C: 450

Option D: 900

Option A: 600

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



Option A: 16

Option B: 64

Option C: 4

Option D: 8

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



Option A: 48

Option B:16

Option C:  a

Option D: None of These

Option B: 16

Vector Questions for JEE Questions No: 8

If the vectors c, â = xi+ yj + zk and b = j are such that a, c and b form a right handed system then is



Option A: z– xk

Option B: 0

Option C: yj

Option D: –zi + xk

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:



Option A: (3/2, 3a × )

Option B: (-3/2, 3c × b)

Option C: (3/2, 3b × )

Option D: (-3/2, 3a × b )

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



Option A: 600

Option B: 300

Option C: 450

Option D: 900

Option A: 600

Vector for JEE Questions No: 11

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



Option A: 0

Option B: 1

Option C: 2

Option D: 3

Option D: 3

JEE Main Math Vector Questions No: 12

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



Option A: 20 units

Option B: 30 units

Option C: 40 units

Option D: 50 units

Option C: 40 units

JEE Mains Vector Questions No: 13

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



Option A: √18

Option B: √72

Option C: √33

Option D: √288

Option C: √33

JEE Mains Math Vector Questions No: 14

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



Option A: Square

Option B: Rhombus

Option C: Rectangle

Option D: None of these

Option D: None of These

Vector Questions for JEE Questions No: 15

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



Option A: 0

Option B: u ∙  v ×  w

Option C: uw × v

Option D: 3 uv × w

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



Option A: 0

Option B: -7

Option C: 7

Option D: 1

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



Option A: cos-1 (19/35)

Option B: cos-1 (17/31)

Option C: 300

Option D: 900

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



Option A: 0

Option B: 2

Option C: -1

Option D: 1

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



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

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



Option A: 3

Option B: 4

Option C: 5

Option D: 9

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



Option A: 1/3

Option B: √2/3

Option C: 2/3

Option D: 2√2/3

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 | uv + w | equals



Option A: 2

Option B: √7

Option C: √14

Option D: 14

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 + 2b + 3c, ????b + 4c and (2???? -1) c are non-coplanar for



Option A: All values of ????

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

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

Option D: No value of ????

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

Vector JEE Main Math Questions No: 24

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



Option A: 40

Option B: 30

Option C: 25

Option D: 15

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 + 3c is collinear with a (???? being some non-zero scalar) then a + 2b + 6c equals



Option A: ????a

Option B: ????b

Option C: ????

Option D: 0

Option D: 0

JEE Mains Vector Questions No: 26

Let ai k , b= xi + j + (1 – x)k and c = yi + xj + (1 + x –  y)k . Then [ a, b, c ]depends on



Option A: Only y

Option B: Only x

Option C: Both x and y

Option D: Neither x and y

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 ???? c ] = [ a b + c b ] for



Option A: Exactly one value of ????

Option B: No value of ????

Option C: Exactly three value of ????

Option D: Exactly two value of ????

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+a+ Ӄ, i +and ci + cj + bk lie in a plane then c is



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

Option A: The Geometric Mean of a and b

JEE Vector Questions No:29

For any vector the value of ( a × i )+ ( a × j )+ ( a × k )is equal to



Option A: 3a

Option B: a

Option C: 2a

Option D: 4a

Option C: 2a

JEE Main Vector Questions No: 30

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



Option A: ( 10/9 )

Option B: ( 10/3√3 )

Option C: ( 3/10 )

Option D: ( 10/3 )