# NCERT Class 12-Mathematics: Chapter – 10 Vector Algebra Part 3 (For CBSE, ICSE, IAS, NET, NRA 2023)

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## Long Answer (L. A)

**Question 8**:

Using vectors, prove that .

**Answer**:

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.

**Answer**:

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)

**Answer**:

(B) Is the correct answer.

**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)

**Answer**:

(D) Is the correct answer.

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

**Answer**:

(A) is the correct answer.