NCERT Solutions for Maths Class 12 Exercise 10.2

# NCERT Solutions for Maths Class 12 Exercise 10.2

Hello Students. In this post, you will find the complete NCERT Solutions for Maths Class 12 Exercise 10.2.

You can download the PDF of NCERT Books Maths Chapter 10 for your easy reference while studying NCERT Solutions for Maths Class 12 Exercise 10.2.

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NCERT Solutions for Maths Class 12 Exercise 10.1

NCERT Solutions for Maths Class 12 Exercise 10.3

NCERT Solutions for Maths Class 12 Exercise 10.2

Maths Class 12 Ex 10.2 Question 1.

Compute the magnitude of the following vectors:

Solution:

Maths Class 12 Ex 10.2 Question 2.

Write two different vectors having same magnitude.

Solution:

There are infinite number of possible answers.

Maths Class 12 Ex 10.2 Question 3.

Write two different vectors having same direction.

Solution:
Let the two vectors are:

Hence, vectors
have the same direction but different magnitude.

There are infinite number of possible answers.

Maths Class 12 Ex 10.2 Question 4.

Find the values of x and y so that the vectors  are equal.

Solution:

We are given  are equal.

If vectors are equal, then their respective components are also equal.

On comparing the components in both the vectors, we get x = 2, y = 3.

Maths Class 12 Ex 10.2 Question 5.

Find the scalar and vector components of the vector with initial point (2, 1) and terminal point (–5, 7).

Solution:
Let A (2, 1) be the initial point and B (–5, 7) be the terminal point.

Maths Class 12 Ex 10.2 Question 6.

Find the sum of the vectors

Solution:

We have,

Thus, the sum of the vectors is

Maths Class 12 Ex 10.2 Question 7.

Find the unit vector in the direction of the vector .

Solution:
We are given that

Maths Class 12 Ex 10.2 Question 8.

Find the unit vector in the direction of vector , where P and Q are the points (1, 2, 3) and (4, 5, 6), respectively.

Solution:
The points P and Q are (1, 2, 3) and (4, 5, 6), respectively.

Maths Class 12 Ex 10.2 Question 9.

For given vectors, , find the unit vector in the direction of the vector .

Solution:

We are given that

Maths Class 12 Ex 10.2 Question 10.

Find a vector in the direction of vector  which has magnitude 8 units.

Solution:
Let the given vector is

Maths Class 12 Ex 10.2 Question 11.

Show that the vectors  are collinear.

Solution:
Let the given vectors are

Since both the vectors have the same direction, they are collinear.

Maths Class 12 Ex 10.2 Question 12.

Find the direction cosines of the vector .

Solution:
Let
Here, a = 1, b = 2, c = 3

Maths Class 12 Ex 10.2 Question 13.

Find the direction cosines of the vector joining the points A (1, 2, –3) and B (–1, –2, 1), directed from A to B.

Solution:
Vector joining the points A and B is

Maths Class 12 Ex 10.2 Question 14.

Show that the vector  are equally inclined to the axes OX, OY, OZ.

Solution:
Let , Direction cosines of vector  are

This shows that the given vector is equally inclined to the axes OX, OY, OZ.

Maths Class 12 Ex 10.2 Question 15.

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are  respectively, in the ratio 2 : 1

(i) internally
(ii) externally.

Solution:
(i) The point R which divides the line joining the pointsin the ratio m : n

Maths Class 12 Ex 10.2 Question 16.

Find the position vector of the midpoint of the vector joining the points P (2, 3, 4) and Q (4, 1, –2).

Solution:

Maths Class 12 Ex 10.2 Question 17.

Show that the points A, B and C with position vectors, , respectively form the vertices of a right angled triangle.

Solution:

Maths Class 12 Ex 10.2 Question 18.

In triangle ABC (figure), which of the following is not true:

Solution:

Using vectors law, we have

Hence, the correct answer is option (C).

Maths Class 12 Ex 10.2 Question 19.

If  are two collinear vectors, then which of the following are incorrect:

(A) , for some scalar Î»

(B)
(C) the respective components of
are proportional.

(D) both the vectors  have same direction, but different magnitudes.

Solution:
Since both the vectors  , being collinear, are not necessarily in the same direction. They may have opposite directions. Their magnitudes may be different.

Hence, the correct answer is option (D).