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

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Long Answer (L.A)

Question 8:

Using vectors, prove that .


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

Fig.10.1-unit vectors making angles

Unit Vectors Making Angles

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].

Fig. 10.2-The three sides of the triangle

The Three Sides of the Triangle

We have

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


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






(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






(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




(D)None of these


(A) is the correct answer.

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