 # NCERT Solution Class 12 Chapter 10- Vector Algebra Exercise 10.3

## NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Exercise 10.3 – Free PDF Download

Exercise 10.3 of NCERT Solutions for Class 12 Maths Chapter 10- Vector Algebra is based on the following topics:

1. Product of Two Vectors
1. Scalar (or dot) product of two vectors: The result of a scalar product of two vectors is a scalar quantity. Two vectors, with magnitudes not equal to zero, are perpendicular if and only if their scalar product is equal to zero.
2. Projection of a vector on a line

Understand these topics better by answering the questions present in the third exercise of Chapter 10- Vector Algebra in the NCERT textbook.

## Download PDF of NCERT Solutions for Class 12 Maths Chapter 10- Vector Algebra Exercise 10.3        ### Access Other Exercises of Class 12 Maths Chapter 10

Exercise 10.1 Solutions 5 Questions

Exercise 10.2 Solutions 19 Questions

Exercise 10.4 Solutions 12 Questions

Miscellaneous Exercise On Chapter 10 Solutions 19 Questions

#### Access Answers to NCERT Class 12 Maths Chapter 10.3

1. Find the angle between two vectors and with magnitudes √3 and 2, respectively having .

Solution:

Firstly let us consider, 2. Find the angle between the vectors Solution:

Let us consider the Hence, the angle between the vectors is cos-1 (5/7).

3. Find the projection of the vector on the vector .

Solution:

Firstly, 4. Find the projection of the vector on the vector .

Solution:

Firstly, Hence, the projection is 60/114.

5. Show that each of the given three vectors is a unit vector: Also, show that they are mutually perpendicular to each other.

Solution:

It is given that   6. Find

Solution:

Let us consider, 7. Evaluate the product Solution:

Let us consider the given expression, 8. Find the magnitude of two vectors , having the same magnitude and such that the angle between them is 60° and their scalar product is ½.

Solution:

Firstly, Hence the magnitude of two vectors is 1. Solution:

Let us consider, Hence the value is 13.

10. If are such that is perpendicular to , then find the value of λ.

Solution:

We know that the 11. Show that is perpendicular to , for any two nonzero vectors .

Solution:

Let us consider, 12. If , then what can be concluded about the vector ?

Solution:

We know 13. If are unit vectors such that , find the value of .

Solution:

Consider the given vectors, Hence the value is -3/2.

14. If either vector , then . But the converse need not be true. Justify your answer with an example.

Solution:

Firstly, 15. If the vertices A, B, C of a triangle ABC are (1, 2, 3), (–1, 0, 0), (0, 1, 2), respectively, then find ∠ABC. [∠ABC is the angle between the vectors and ]

Solution:

We know Hence, the angle is cos-1 (10/102).

16. Show that the points A (1, 2, 7), B (2, 6, 3) and C (3, 10, –1) are collinear.

Solution:

Let us consider

Given points are A (1, 2, 7), B (2, 6, 3), and C (3, 10, –1).

Now, Therefore, the given points A, B, and C are collinear.

17. Show that the vectors form the vertices of a right angled triangle.

Solution:

Firstly consider,  Solution:

Explanation: 