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:
- Product of Two Vectors
- 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 only if their scalar product is equal to zero.
- 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.
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:
First, 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:
First,
4. Find the projection of the vector
on the vector
.
Solution:
First,
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:
First,
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:
First,
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:
First, consider
Solution:
Explanation:
Also, explore –Â
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