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QUESTION: 1

Zero Vector

Solution:

A vector whose initial and terminal points coincides is called Zero Vector. The magnitude of Zero Vector is also Zero.

QUESTION: 2

If a vector is expressed in component form as then the magnitude of the vector is

Solution:

QUESTION: 3

Find the value of x for which x is a unit vector

Solution:

QUESTION: 4

Find the angle between two vectors

Solution:

QUESTION: 5

Find λ and μ if

Solution:

It is given that:

QUESTION: 6

Unit Vector is

Solution:

The vector whose magnitude is always 1 or unity is called a Unit Vector.

QUESTION: 7

If a vector is expressed in component form as then x, y and z are referred to as

Solution:

In x , y and z represents the components of along x-axis ,y-axis and z-axis respectively.

QUESTION: 8

Show that the points A(1, – 2, – 8), B (5, 0, – 2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.

Solution:

Therefore , AB and BC are parallel, but point B is common , so points , A,B,C are collinear. As

QUESTION: 9

Find the projection of the vector

Solution:

QUESTION: 10

Let the vectors be such that is a unit vector if the angle between vectors is

Solution:

QUESTION: 11

The unit vector in the direction of a given vector

Solution:

is called the unit vector of a given vector

QUESTION: 12

Which of the following is a vector?

Solution:

Acceleration is a vector quantity , because acceleration is defined as the rate of change of velocity w.r.t. time.

QUESTION: 13

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are externally in the ratio 1 : 2. Also, show that P is the mid point of the line segment RQ.

Solution:

Let position vector of point R be . As point R divides externally the line segment PQ in the ratio 1:2 .therefore ,

Also , mid point of the line segment RQ is :

Which is the position vector of point P.

Therefore , P is the mid point of line segment RQ.

QUESTION: 14

Find the projection of the vector on the vector

Solution:

then projection of vector a on vector b is given by :

QUESTION: 15

If θ is the angle between two vectors

Solution:

QUESTION: 16

Coinitial Vectors are

Solution:

Two vectors whose initial point is same are called co- initial vectors

QUESTION: 17

In the figure which are the Equal vectors?

Solution:

are equal vectors , because they have equal magnitude and same direction.

QUESTION: 18

The scalar product of two nonzero vectors

Solution:

The scalar product of two nonzero vectors by

QUESTION: 19

Find if for a unit vector

Solution:

QUESTION: 20

If θ is the angle between any two vectors when θ is equal to

Solution:

QUESTION: 21

Vectors A and BareCollinear

Solution:

Two vectors A and B are said to be collinear , if they are parallel to the same line irrespective of their magnitudes and directions.

QUESTION: 22

Solution:

collinear vectors , because they are parallel in direction and having the same magnitude.

QUESTION: 23

The scalar product of two nonzero vectors

Solution:

The scalar product of two nonzero vectors :

QUESTION: 24

If are unit vectors such that then, the value of

Solution:

It is given that : are unit vectors such that

then :

QUESTION: 25

Find the area of the triangle with vertices A(1, 1, 2), B(2, 3, 5) and C(1, 5, 5).

Solution:

Therefore , the area of triangle

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