# NCERT Solution Class 12 Chapter 10- Vector Algebra Miscellaneous Exercise

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

The Miscellaneous Exercise of NCERT Solutions for Class 12 Maths Chapter 10- Vector Algebra is based on all the topics covered in this chapter. The main topics that are covered in this chapter include:

1. Basic Concepts of Vector Algebra
2. Types of Vectors
3. Addition of Vectors
4. Multiplication of a Vector by a Scalar
5. Product of Two Vectors

Miscellaneous exercise provides questions from all the topics in the chapter. Solving these questions helps the students in a quick revision of the chapter.

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

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

Exercise 10.1 Solutions 5 Questions

Exercise 10.2 Solutions 19 Questions

Exercise 10.3 Solutions 18 Questions

Exercise 10.4 Solutions 12 Questions

#### Access Answers to NCERT Class 12 Maths Chapter 10 Vector Algebra Miscellaneous Exercise

1. Write down a unit vector in XY-plane, making an angle of 30Â° with the positive direction ofÂ x-axis.

Solution:

Let us consider,

2. Find the scalar components and magnitude of the vector joining the points P (x1, y1, z1) and Q (x2, y2, z2).

Solution:

Firstly let us consider,

3. A girl walks 4 km towards west, then she walks 3 km in a direction 30Â° east of north and stops. Determine the girlâ€™s displacement from her initial point of departure.

Solution:

It is given that,

Let O and B be the initial and final positions of the girl respectively.

Then, the girlâ€™s position can be shown as:

4. If, then is it true that? Justify your answer.

Solution:

It is given that,

5. Find the value ofÂ xÂ for whichis a unit vector.

Solution:

We know,

6. Find a vector of magnitude 5 units, and parallel to the resultant of the vectors

.

Solution:

Let us consider the,

7. If, find a unit vector parallel to the vector.

Solution:

Let us consider the given vectors,

8. Show that the points A (1, â€“2, â€“8), B (5, 0, â€“2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.

Solution:

Firstly let us consider,

9. Find the position vector of a point R which divides the line joining two points P and Q whose position vectors areexternally in the ratio 1: 2. Also, show that P is the midpoint of the line segment RQ.

Solution:

We know,

10. The two adjacent sides of a parallelogram areandÂ .

Find the unit vector parallel to its diagonal. Also, find its area.

Solution:

Firstly let us consider,

11. Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are.

Solution:

Firstly,

Letâ€™s assume a vector to be equally inclined to axes OX, OY, and OZ at angleÂ Î±.

Then, the direction cosines of the vector are cosÂ Î±, cosÂ Î±, and cosÂ Î±.

Now, we know that

Therefore, the direction cosines of the vector which are equally inclined to the axes are

Hence proved.

Solution:

Assume,

13. The scalar product of the vectorwith a unit vector along the sum of vectorsÂ andÂ is equal to one. Find the value of.

Solution:

Letâ€™s consider the

14. IfÂ are mutually perpendicular vectors of equal magnitudes, show that the vectorÂ is equally inclined toÂ and.

Solution:

Lets assume,

Hence proved.

15. Prove that, if and only ifÂ are perpendicular, given.

Solution:

It is given that

Hence proved.

Solution:

Explanation:

Solution:

Explanation:

Hence the correct answer is D.

18. The value ofÂ is

(A) 0 (B) â€“1 (C) 1 (D) 3

Solution:

Explanation:

It is given that,

Hence the correct answer is C.

Solution:

Explanation: