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

## NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Miscellaneous Exercise – 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 the following:

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

The miscellaneous exercise provides questions from all the topics covered in the chapter. So, solving these questions helps the students in a quick revision of the chapter.

## Download the 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 30° with the positive direction of the 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:

First, let us consider, 3. A girl walks 4 km towards the west, then she walks 3 km in a direction 30° east of the north and stops. Determine the girl’s displacement from her initial point of departure.

Solution:

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

Then, the girl’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 of x, for which is 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, –2, –8), B (5, 0, –2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.

Solution:

First, 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 are externally 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 are and .

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:

First,

Let’s assume a vector to be equally inclined to axes OX, OY, and OZ at angle α.

Then, the direction cosines of the vector are cos α, cos α, and cos α.

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 vector with a unit vector along the sum of vectors and is equal to one. Find the value of .

Solution:

Let’s consider the 14. If are mutually perpendicular vectors of equal magnitudes, show that the vector is equally inclined to and .

Solution:

Let’s assume, Hence proved.

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

Solution:

It is given that Hence proved. Solution:

Explanation:   Solution:

Explanation: Hence the correct answer is D.

18. The value of is

(A) 0, (B) –1, (C), 1 (D) 3

Solution:

Explanation:

It is given that, Hence, the correct answer is C. Solution:

Explanation: 