NCERT Class 12-Mathematics: Chapter – 10 Vector Algebra Part 3 (For CBSE, ICSE, IAS, NET, NRA 2022)

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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

Fig. 10.1-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

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.