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

Get unlimited access to the best preparation resource for CBSE/Class-12 Business-Studies: fully solved questions with step-by-step explanation- practice your way to success.

Download PDF of This Page (Size: 191K)

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

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.

Answer:

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

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.

Developed by: