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# Test: Vector Algebra (Competition Level) - 3

## 25 Questions MCQ Test Mathematics (Maths) Class 12 | Test: Vector Algebra (Competition Level) - 3

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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. The solved questions answers in this Test: Vector Algebra (Competition Level) - 3 quiz give you a good mix of easy questions and tough questions. JEE students definitely take this Test: Vector Algebra (Competition Level) - 3 exercise for a better result in the exam. You can find other Test: Vector Algebra (Competition Level) - 3 extra questions, long questions & short questions for JEE on EduRev as well by searching above.
QUESTION: 1

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QUESTION: 2

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QUESTION: 3

### simplifies to

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QUESTION: 4

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

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QUESTION: 5

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

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QUESTION: 6

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

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QUESTION: 7

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

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QUESTION: 8

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QUESTION: 9

Consider a tetrahedron with faces f1, f2, f3, fLet ​ be the vectors whose magnitudes are respectively equalt to the areas of  f1, f2, f3, f4 and  whose directions are perpendicular to these faces in the outward direction. Then

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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

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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

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QUESTION: 15

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

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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

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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

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QUESTION: 19

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

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QUESTION: 20

If A1, A2, A3, .........Aare 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

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*Multiple options can be correct
QUESTION: 22

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

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*Multiple options can be correct
QUESTION: 23

The vector  is

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*Multiple options can be correct
QUESTION: 24

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

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QUESTION: 25

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

Solution: