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Test: Vector Algebra- 1


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25 Questions MCQ Test Mathematics (Maths) Class 12 | Test: Vector Algebra- 1

Test: Vector Algebra- 1 for JEE 2022 is part of Mathematics (Maths) Class 12 preparation. The Test: Vector Algebra- 1 questions and answers have been prepared according to the JEE exam syllabus.The Test: Vector Algebra- 1 MCQs are made for JEE 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Vector Algebra- 1 below.
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Test: Vector Algebra- 1 - Question 1

Vector has

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A vector has both magnitude as well as direction.

Test: Vector Algebra- 1 - Question 2

Correct form of distributive law is

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Distributive law is given by : 

Test: Vector Algebra- 1 - Question 3

Magnitude of the vector 

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We have :

Test: Vector Algebra- 1 - Question 4

Find the unit vector in the direction of vector  where P and Q are the points (1, 2, 3) and (4, 5, 6), respectively

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Test: Vector Algebra- 1 - Question 5

If  is a non zero vector of magnitude ‘a’ and λ a non zero scalar, then λ is a unit vector if

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λ is a unit vector if and only if  is equal to 

Test: Vector Algebra- 1 - Question 6

Find the values of x and y so that the vectors  are equal

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Test: Vector Algebra- 1 - Question 7

If P1(x1, y1, z1) and P2(x2, y2, z2) are any two points, then the vector joining P1 and P2is the vector P1P2. Magnitude of the vector 

Detailed Solution for Test: Vector Algebra- 1 - Question 7

If P1(x1, y1, z1) and P2(x2, y2, z2) are any two points, then the vector joining P1 and P2is the vector P1P2, then ;

Test: Vector Algebra- 1 - Question 8

Find the scalar and vector components of the vector with initial point (2, 1) and terminal point (– 5, 7). 

Detailed Solution for Test: Vector Algebra- 1 - Question 8

The scalar and vector components of the vector with initial point (2, 1) and terminal point (– 5, 7) is given by : (- 5 – 2) i.e. – 7 and (7 – 1) i.e. 6. Therefore, the scalar components are – 7 and 6 .,and vector components are 

Test: Vector Algebra- 1 - Question 9

Find a vector in the direction of the vector  which has a magnitude of 8 units

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Test: Vector Algebra- 1 - Question 10

Find , if   and  

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Test: Vector Algebra- 1 - Question 11

Direction angles are angles

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α,β,γ are the angles which the position vector  makes with the positive x-axis ,y-axis and z-axis respectively are called direction angles.

Test: Vector Algebra- 1 - Question 12

 are any three vectors then the correct expression for distributivity of scalar product over addition is

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 are any three vectors then the correct expression for distributivity of scalar product over addition is :

Test: Vector Algebra- 1 - Question 13

Find the values of x and y so that the vectors 

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Test: Vector Algebra- 1 - Question 14

Find the direction cosines of the vector 

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Test: Vector Algebra- 1 - Question 15

Find a unit vector perpendicular to each of 

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It is given that: 








Therefore, the unit vector perpendicular to both the vectors and

Test: Vector Algebra- 1 - Question 16

Direction cosines

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Cosines of the angles α,β,γ are called direction cosines.

Test: Vector Algebra- 1 - Question 17

Magnitude of the vector 

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We have : 

Test: Vector Algebra- 1 - Question 18

Find the sum of the vectors    and  

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We have: 

Test: Vector Algebra- 1 - Question 19

Find the direction cosines of the vector joining the points A(1, 2, –3) and B(–1, –2, 1), directed from A to B.

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Therefore, the D.C.’s of vector AB are given by: 

Test: Vector Algebra- 1 - Question 20

If a unit vector makes angles π/3 with   and an acute angle θ with  then find θ

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Test: Vector Algebra- 1 - Question 21

If l, m and n are direction cosines of the position vector OP the coordinates of P are

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If l , m and n are the direction cosines of vector  then , the coordinates of point P are given by : lr ,mr and nr respectively.

Test: Vector Algebra- 1 - Question 22

Unit vectors along the axes OX, OY and OZ are denoted by 

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represents the unit vectors along the co ordinate axis i.e. OX ,OY and OZ respectively.

Test: Vector Algebra- 1 - Question 23

Write down a unit vector in XY-plane, making an angle of 30° with the positive direction of x-axis.

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Test: Vector Algebra- 1 - Question 24

Find the angle between two vectors  with magnitudes and 2, respectively, having 

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Test: Vector Algebra- 1 - Question 25

If a unit vector  makes angles and an acute angle θ with , then the components of  are

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Let  It is given that left| , then , 





Putting these values in (1) , we get : 



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