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

ncert sol Class 12 maths chapter 10 ex 3 1
ncert sol Class 12 maths chapter 10 ex 3 2
ncert sol Class 12 maths chapter 10 ex 3 3
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ncert sol Class 12 maths chapter 10 ex 3 5
ncert sol Class 12 maths chapter 10 ex 3 6
ncert sol Class 12 maths chapter 10 ex 3 7
ncert sol Class 12 maths chapter 10 ex 3 8

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 12 Mathematics
Chapter 10- image 54andNCERT Solutions Class 12 Mathematics
Chapter 10- image 55with magnitudes √3 and 2, respectively havingNCERT Solutions Class 12 Mathematics
Chapter 10- image 56.

Solution:

Firstly let us consider,

NCERT Solutions Class 12 Mathematics
Chapter 10- image 57

2. Find the angle between the vectorsNCERT Solutions Class 12 Mathematics
Chapter 10- image 58

Solution:

Let us consider the

NCERT Solutions Class 12 Mathematics
Chapter 10- image 59

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

3. Find the projection of the vectorNCERT Solutions Class 12 Mathematics
Chapter 10- image 60on the vectorNCERT Solutions Class 12 Mathematics
Chapter 10- image 61.

Solution:

Firstly,

NCERT Solutions Class 12 Mathematics
Chapter 10- image 62

4. Find the projection of the vectorNCERT Solutions Class 12 Mathematics
Chapter 10- image 63on the vectorNCERT Solutions Class 12 Mathematics
Chapter 10- image 64.

Solution:

Firstly,

NCERT Solutions Class 12 Mathematics
Chapter 10- image 65

Hence, the projection is 60/114.

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

NCERT Solutions Class 12 Mathematics
Chapter 10- image 66

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

Solution:

It is given that

NCERT Solutions Class 12 Mathematics
Chapter 10- image 67

NCERT Solutions Class 12 Mathematics
Chapter 10- image 68

NCERT Solutions Class 12 Mathematics
Chapter 10- image 696. Find

Solution:

Let us consider,

NCERT Solutions Class 12 Mathematics
Chapter 10- image 70

7. Evaluate the productNCERT Solutions Class 12 Mathematics
Chapter 10- image 71

Solution:

Let us consider the given expression,

NCERT Solutions Class 12 Mathematics
Chapter 10- image 72

8. Find the magnitude of two vectorsNCERT Solutions Class 12 Mathematics
Chapter 10- image 73, having the same magnitude and such that the angle between them is 60° and their scalar product is ½.

Solution:

Firstly,

NCERT Solutions Class 12 Mathematics
Chapter 10- image 74

Hence the magnitude of two vectors is 1.

NCERT Solutions Class 12 Mathematics
Chapter 10- image 75

Solution:

Let us consider,

NCERT Solutions Class 12 Mathematics
Chapter 10- image 76

Hence the value is 13.

10. IfNCERT Solutions Class 12 Mathematics
Chapter 10- image 77are such thatNCERT Solutions Class 12 Mathematics
Chapter 10- image 78is perpendicular toNCERT Solutions Class 12 Mathematics
Chapter 10- image 79, then find the value of λ.

Solution:

We know that the

NCERT Solutions Class 12 Mathematics
Chapter 10- image 80

11. Show that NCERT Solutions Class 12 Mathematics
Chapter 10- image 81is perpendicular toNCERT Solutions Class 12 Mathematics
Chapter 10- image 82, for any two nonzero vectorsNCERT Solutions Class 12 Mathematics
Chapter 10- image 83.

Solution:

Let us consider,

NCERT Solutions Class 12 Mathematics
Chapter 10- image 84

12. IfNCERT Solutions Class 12 Mathematics
Chapter 10- image 85, then what can be concluded about the vectorNCERT Solutions Class 12 Mathematics
Chapter 10- image 86?

Solution:

We know

NCERT Solutions Class 12 Mathematics
Chapter 10- image 87

13. If NCERT Solutions Class 12 Mathematics
Chapter 10- image 88are unit vectors such that NCERT Solutions Class 12 Mathematics
Chapter 10- image 89, find the value of NCERT Solutions Class 12 Mathematics
Chapter 10- image 90.

Solution:

Consider the given vectors,

NCERT Solutions Class 12 Mathematics
Chapter 10- image 91

Hence the value is -3/2.

14. If either vectorNCERT Solutions Class 12 Mathematics
Chapter 10- image 92, thenNCERT Solutions Class 12 Mathematics
Chapter 10- image 93. But the converse need not be true. Justify your answer with an example.

Solution:

Firstly,

NCERT Solutions Class 12 Mathematics
Chapter 10- image 94

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 12 Mathematics
Chapter 10- image 95andNCERT Solutions Class 12 Mathematics
Chapter 10- image 96]

Solution:

We know

NCERT Solutions Class 12 Mathematics
Chapter 10- image 97

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,

NCERT Solutions Class 12 Mathematics
Chapter 10- image 98

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

17. Show that the vectorsNCERT Solutions Class 12 Mathematics
Chapter 10- image 99form the vertices of a right angled triangle.

Solution:

Firstly consider,

NCERT Solutions Class 12 Mathematics
Chapter 10- image 100

NCERT Solutions Class 12 Mathematics
Chapter 10- image 101

Solution:

Explanation:

NCERT Solutions Class 12 Mathematics
Chapter 10- image 102

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