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

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 includes:

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

Miscellaneous exercise provides questions from all the topics provided 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

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 of Maths NCERT Class 12 Chapter 10 Miscellaneous

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

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

Solution: 3. A girl walks 4 km towards west, then she walks 3 km in a direction 30° east of 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:  5. Find the value of x for which is a unit vector.

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

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

Solution: 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:  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 mid point of the line segment RQ.

Solution: 10. The two adjacent sides of a parallelogram are and .

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

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

Solution:

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.

Now, we know that Therefore, the direction cosines of the vector which are equally inclined to the axes are .

12. Let and . Find a vector which is perpendicular to both and , and .

Solution:  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 λ.

Solution: 14. If are mutually perpendicular vectors of equal magnitudes, show that the vector is equally inclined to and .

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

Solution: 16. If θ is the angle between two vectors and , then only when Solution: 17. Let and be two unit vectors andθ is the angle between them. Then is a unit vector if Solution: 18. The value of is

(A) 0 (B) –1 (C) 1 (D) 3

Solution:

Given, 19. If θ is the angle between any two vectors and , then when θ is equal to Solution: #### 1 Comment

1. dayalan

excellent work