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This mock test of Test: Vector Algebra (Competition Level) - 3 for JEE helps you for every JEE entrance exam.
This contains 25 Multiple Choice Questions for JEE Test: Vector Algebra (Competition Level) - 3 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

If line is parallel to the plane , then the value of m is

Solution:

QUESTION: 2

Given , then

Solution:

QUESTION: 3

simplifies to

Solution:

QUESTION: 4

Let be a vector perpendicular to , where then (ℓ +m+n) is equal to

Solution:

QUESTION: 5

If are three non-coplaner non-zero vectors and is any vector in space, then is equal to

Solution:

QUESTION: 6

If a, b, c are pth, qth, rth terms of an H.P and

Solution:

QUESTION: 7

If the unit vectors are inclined at an angle 2θ and , then for θ ∈ [0, π], θ may lie in the interval

Solution:

QUESTION: 8

Solution:

QUESTION: 9

Consider a tetrahedron with faces f_{1}, f_{2}, f_{3}, f_{4 }Let be the vectors whose magnitudes are respectively equalt to the areas of f_{1}, f_{2}, f_{3}, f_{4} and whose directions are perpendicular to these faces in the outward direction. Then

Solution:

QUESTION: 10

Let be non-coplaner unit vectors equally inclined to one another at an acute angle θ. Then in terms of θ is equalt to

Solution:

QUESTION: 11

Let and . If the vector lies in the plane of , then x equals

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QUESTION: 12

Images of the point P with position vector ^{ }in the line whose vector equation is has the position vector

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QUESTION: 13

Let be such that . If the projection is equal to that of are perpendicular to each other, then equals.

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QUESTION: 14

Let and . If is a unit vector such that then is equal to

Solution:

QUESTION: 15

Equation of a line which passes through a point with position vector , parallel to the plane and perpendicular to the line

Solution:

QUESTION: 16

Points L, M and N lie on the sides AB, BC and CA of the triangle ABC such that ℓ(AL) : ℓ(LB) = ℓ(BM) :ℓ(MC) = ℓ(CN) : ℓ(NA) = m :n, then the areas of the triangles LMN and ABC are in the ratio

Solution:

QUESTION: 17

is equal to

Solution:

**ANSWER :- c**

**Solution :- [a×b b×c c×a] **

**= (a×b) . [(b×c) * (c×a)]**

**= (a×b) [(b×c) . a(c) - (b×c) . c]**

**= (a×b) [(b×c) . a(c) - 0]**

**= [(a×b) . c] [(b×c) . a]**

**= [a b c] [(b c a]**

**= - [a b c] [(a c b]**

**= [a b c] [(a b c ] => [a b c]^2**

QUESTION: 18

If the vectors (a ≠ b ≠ c ≠ 1) are coplanar, then the value of is equal to

Solution:

QUESTION: 19

The vectors are coinitial. The vector which is bisecting the angle between the vectors and is having the magnitude √6 is

Solution:

QUESTION: 20

If A_{1}, A_{2}, A_{3}, .........A_{n }are the vertics of a regular plane polygon with n sides and O is its centre then equals

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QUESTION: 21

For any four points P,Q, R, S, is equal to 4 times the

area of the triangle

Solution:

*Multiple options can be correct

QUESTION: 22

If a line has a vector equation , then which of the following statements hold goods ?

Solution:

*Multiple options can be correct

QUESTION: 23

The vector is

Solution:

*Multiple options can be correct

QUESTION: 24

The vector directed along the external bisector of the angle between the vectors and with

Solution:

QUESTION: 25

Which of the following acts in accordance with right hand screw rule?

Solution:

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