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

## NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Exercise 10.3 â€“ 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 vectorsandwith magnitudes âˆš3 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 vectoron the vector.

Solution:

Firstly,

4. Find the projection of the vectoron the vector.

Solution:

Firstly,

Hence, the projection is 60/âˆš114.

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 60Â° and their scalar product is Â½.

Solution:

Firstly,

Hence the magnitude of two vectors is 1.

Solution:

Let us consider,

Hence the value is âˆš13.

10. Ifare such thatis perpendicular to, then find the value ofÂ Î».

Solution:

We know that the

11. Show thatÂ 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. IfÂ are unit vectors such thatÂ , find the value ofÂ .

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), (â€“1, 0, 0), (0, 1, 2), respectively, then find âˆ ABC. [âˆ ABC is the angle between the vectorsand]

Solution:

We know

Hence, the angle is cos-1 (10/ âˆš102).

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

Solution:

Let us consider

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

Now,

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

17. Show that the vectorsform the vertices of a right angled triangle.

Solution:

Firstly consider,

Solution:

Explanation: