# NCERT Class 12-Mathematics: Chapter –10 Vector Algebra Part 3

Question 8:

Using vectors, prove that .

Let be unit vectors making angles A and B, respectively, with positive direction of x-axis. Then

We know

By definition

In terms of components, we have

From (1) and (2), we get

.

Question 9:

Prove that in a , where a, b, c represent the magnitudes of the sides opposite to vertices A, B, C, respectively.

Let the three sides of the triangle BC, CA and AB be represented by and respectively [Fig. 10.2].

We have

Which pre cross multiplying by , and post cross multiplying by , gives

and

respectively. Therefore,

Dividing by , we get

## Objective Type Questions

### Choose the Correct Answer from the Given Four Options in Each of the Examples 10 to 21

Question 10:

The magnitude of the vector is

(A)

(B)

(C)

(D)

Question 11:

The position vector of the point which divides the join of points with position vectors and in the ratio is

(A)

(B)

(C)

(D)

Applying section formula the position vector of the required point is

Question 12:

The vector with initial point and terminal point is

(A)

(B)

(C)

(D)None of these