# NCERT Solutions for Class 12 Maths Chapter 10- Vector Algebra Exercise 10.2

## NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Exercise 10.2 â€“ CBSE Free PDF Download

Exercise 10.2 of NCERT Solutions for Class 12 Maths Chapter 10- Vector Algebra is based on the following topics:

2. Multiplication of a Vector by a Scalar
1. Components of a vector
2. Vector joining two points
3. Section formula

All these topics can be understood thoroughly by solving the problems given in this exercise. The solutions of all the problems of this exercise are given here.

## Download PDF of NCERT Solutions for Class 12 Maths Chapter 10- Vector Algebra Exercise 10.2

### Access Other Exercises of Class 12 Maths Chapter 10

Exercise 10.1 Solutions 5 Questions

Exercise 10.3 Solutions 18 Questions

Exercise 10.4 Solutions 12 Questions

Miscellaneous Exercise On Chapter 10 Solutions 19 Questions

#### Access Answers to NCERT Class 12 Maths Chapter 10 Exercise 10.2

1. Compute the magnitude of the following vectors:

Solution:

Given vectors are:

2. Write two different vectors having same magnitude.

Solution:

3. Write two different vectors having same direction.

Solution:

Two different vectors having same directions are:

Let us

4. Find the values ofÂ xÂ andÂ yÂ so that the vectorsÂ are equal

Solution:

Given vectors
will be equal only if their corresponding components are equal.

Thus, the required values ofÂ xÂ andÂ yÂ are 2 and 3 respectively.

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

Solution:

The scalar and vector components are:

The vector with initial point P (2, 1) and terminal point Q (â€“5, 7) can be shown as,

Thus, the required scalar components are â€“7 and 6 while the vector components are

6. Find the sum of the vectors

Solution:

Let us find the sum of the vectors:

7. Find the unit vector in the direction of the vector

Solution:

We know that

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:

We know that,

9. For given vectors,Â andÂ , find the unit vector in the direction of the vectorÂ

Solution:

We know that,

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

Solution:

Firstly,

11. Show that the vectorsare collinear.

Solution:

Firstly,

Therefore, we can say that the given vectors are collinear.

12. Find the direction cosines of the vectorÂ

Solution:

Firstly,

13. Find the direction cosines of the vector joining the points A (1, 2, â€“3) and

B (â€“1, â€“2, 1) directed from A to B.

Solution:

We know that the

Given points are A (1, 2, â€“3) and B (â€“1, â€“2, 1).

Now,

14. Show that the vectorÂ is equally inclined to the axes OX, OY, and OZ.

Solution:

Firstly,

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

(i) internally

(ii) externally

Solution:

We know that

The position vector of point R dividing the line segment joining two points

P and Q in the ratioÂ m:Â nÂ is given by:

16. Find the position vector of the mid point of the vector joining the points P (2, 3, 4) and Q (4, 1, â€“ 2).

Solution:

The position vector of mid-point R of the vector joining points P (2, 3, 4) and Q (4, 1, â€“ 2) is given by,

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

Solution:

We know

Given position vectors of points A, B, and C are:

Hence, proved that the given points form the vertices of a right angled triangle.

18. In triangle ABC (Fig 10.18) which of the following isÂ notÂ true:

Solution:

Firstly let us consider,

19. IfÂ are two collinear vectors, then which of the following areÂ incorrect:

A.Â , for some scalar Î»

B.Â

C.Â the respective components ofÂ are proportional

D.Â both the vectorsÂ have same direction, but different magnitudes

Solution:

We know