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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

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

A vector has both magnitude as well as direction.

Test: Vector Algebra- 1 - Question 2

### Correct form of distributive law is

Detailed Solution for Test: Vector Algebra- 1 - Question 2

Distributive law is given by : Test: Vector Algebra- 1 - Question 3

### Magnitude of the vector Detailed Solution for Test: Vector Algebra- 1 - Question 3

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

Detailed Solution for Test: Vector Algebra- 1 - Question 4   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

Detailed Solution for Test: Vector Algebra- 1 - Question 5

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

Detailed Solution for Test: Vector Algebra- 1 - Question 6 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

Detailed Solution for Test: Vector Algebra- 1 - Question 9    Test: Vector Algebra- 1 - Question 10

Find , if and Detailed Solution for Test: Vector Algebra- 1 - Question 10  Test: Vector Algebra- 1 - Question 11

Direction angles are angles

Detailed Solution for Test: Vector Algebra- 1 - Question 11

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

Detailed Solution for Test: Vector Algebra- 1 - Question 12 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 Detailed Solution for Test: Vector Algebra- 1 - Question 13 Test: Vector Algebra- 1 - Question 14

Find the direction cosines of the vector Detailed Solution for Test: Vector Algebra- 1 - Question 14   Test: Vector Algebra- 1 - Question 15

Find a unit vector perpendicular to each of  Detailed Solution for Test: Vector Algebra- 1 - Question 15

It is given that:     Therefore, the unit vector perpendicular to both the vectors and Test: Vector Algebra- 1 - Question 16

Direction cosines

Detailed Solution for Test: Vector Algebra- 1 - Question 16

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

Test: Vector Algebra- 1 - Question 17

Magnitude of the vector Detailed Solution for Test: Vector Algebra- 1 - Question 17

We have : Test: Vector Algebra- 1 - Question 18

Find the sum of the vectors  and Detailed Solution for Test: Vector Algebra- 1 - Question 18

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.

Detailed Solution for Test: Vector Algebra- 1 - Question 19     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

Detailed Solution for Test: Vector Algebra- 1 - Question 20     Test: Vector Algebra- 1 - Question 21

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

Detailed Solution for Test: Vector Algebra- 1 - Question 21

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

Detailed Solution for Test: Vector Algebra- 1 - Question 22 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.

Detailed Solution for Test: Vector Algebra- 1 - Question 23 Test: Vector Algebra- 1 - Question 24

Find the angle between two vectors with magnitudes and 2, respectively, having Detailed Solution for Test: Vector Algebra- 1 - Question 24  Test: Vector Algebra- 1 - Question 25

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

Detailed Solution for Test: Vector Algebra- 1 - Question 25

Let It is given that left| , then ,       Putting these values in (1) , we get :    ## Mathematics (Maths) Class 12

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## Mathematics (Maths) Class 12

209 videos|209 docs|139 tests