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# Competition Level Test: Vector Algebra- 2

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## 25 Questions MCQ Test Mathematics (Maths) Class 12 | Competition Level Test: Vector Algebra- 2

Competition Level Test: Vector Algebra- 2 for JEE 2023 is part of Mathematics (Maths) Class 12 preparation. The Competition Level Test: Vector Algebra- 2 questions and answers have been prepared according to the JEE exam syllabus.The Competition Level Test: Vector Algebra- 2 MCQs are made for JEE 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Competition Level Test: Vector Algebra- 2 below.
Solutions of Competition Level Test: Vector Algebra- 2 questions in English are available as part of our Mathematics (Maths) Class 12 for JEE & Competition Level Test: Vector Algebra- 2 solutions in Hindi for Mathematics (Maths) Class 12 course. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free. Attempt Competition Level Test: Vector Algebra- 2 | 25 questions in 50 minutes | Mock test for JEE preparation | Free important questions MCQ to study Mathematics (Maths) Class 12 for JEE Exam | Download free PDF with solutions
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Competition Level Test: Vector Algebra- 2 - Question 1

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

Competition Level Test: Vector Algebra- 2 - Question 2

### Given   , then

Competition Level Test: Vector Algebra- 2 - Question 3

### simplifies to

Competition Level Test: Vector Algebra- 2 - Question 4

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

Competition Level Test: Vector Algebra- 2 - Question 5

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

Competition Level Test: Vector Algebra- 2 - Question 6

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

Competition Level Test: Vector Algebra- 2 - Question 7

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

Competition Level Test: Vector Algebra- 2 - Question 8

Competition Level Test: Vector Algebra- 2 - 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

Competition Level Test: Vector Algebra- 2 - 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

Competition Level Test: Vector Algebra- 2 - Question 11

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

Competition Level Test: Vector Algebra- 2 - Question 12

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

Competition Level Test: Vector Algebra- 2 - Question 13

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

Competition Level Test: Vector Algebra- 2 - Question 14

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

Competition Level Test: Vector Algebra- 2 - Question 15

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

Competition Level Test: Vector Algebra- 2 - 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

Competition Level Test: Vector Algebra- 2 - Question 17

is equal to

Detailed Solution for Competition Level Test: Vector Algebra- 2 - Question 17

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

Competition Level Test: Vector Algebra- 2 - Question 18

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

Competition Level Test: Vector Algebra- 2 - Question 19

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

Competition Level Test: Vector Algebra- 2 - Question 20

If A1, A2, A3, .........Aare the vertics of a regular plane polygon with n sides and O is its centre then  equals

Competition Level Test: Vector Algebra- 2 - Question 21

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

area of the triangle

*Multiple options can be correct
Competition Level Test: Vector Algebra- 2 - Question 22

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

*Multiple options can be correct
Competition Level Test: Vector Algebra- 2 - Question 23

The vector  is

*Multiple options can be correct
Competition Level Test: Vector Algebra- 2 - Question 24

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

Competition Level Test: Vector Algebra- 2 - Question 25

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

## Mathematics (Maths) Class 12

209 videos|218 docs|139 tests
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## Mathematics (Maths) Class 12

209 videos|218 docs|139 tests