NCERT Solution Class 12 Chapter 10- Vector Algebra Exercise 10.3

The 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

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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 of Maths NCERT Class 12 Chapter 10.3

1. Find the angle between two vectorsNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 1andNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 2with magnitudes √3 and 2, respectively havingNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 3.

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 4

2. Find the angle between the vectorsNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 5

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 6

3. Find the projection of the vectorNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 7on the vectorNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 8.

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 9

4. Find the projection of the vectorNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 10on the vectorNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 11.

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 12

5. Show that each of the given three vectors is a unit vector:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 13

Also, show that they are mutually perpendicular to each other.

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 14

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 15

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 166. Find

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 17

7. Evaluate the productNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 18

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 19

8. Find the magnitude of two vectorsNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 20, having the same magnitude and such that the angle between them is 60° and their scalar product is ½.

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 21

9. FindNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 23, if for a unit vectorNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 22

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 24

10. IfNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 25are such thatNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 26is perpendicular toNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 27, then find the value of λ.

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 28

11. Show that NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 29is perpendicular toNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 30, for any two nonzero vectorsNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 31.

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 32

12. IfNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 33, then what can be concluded about the vectorNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 34?

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 35

13. If NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 36are unit vectors such that NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 37, find the value of NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 38.

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 39

14. If either vectorNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 40, thenNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 41. But the converse need not be true. Justify your answer with an example.

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 42

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 vectorsNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 43andNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 44]

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 45

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

Solution:

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

Now,

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 46

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

17. Show that the vectorsNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 47form the vertices of a right angled triangle.

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 48

18. IfNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra - 2is a nonzero vector of magnitude ‘a’ and λ a nonzero scalar, then λNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 49is unit vector if

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 50

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.3 - 51

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