NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Ex 10.3

NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Ex 10.3 are part of NCERT Solutions for Class 12 Maths. Here we have given NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Ex 10.3.

• Vector Algebra Class 12 Ex 10.1
• Vector Algebra Class 12 Ex 10.2
• Vector Algebra Class 12 Ex 10.4

Board	CBSE
Textbook	NCERT
Class	Class 12
Subject	Maths
Chapter	Chapter 10
Chapter Name	Vector Algebra
Exercise	Ex 10.3
Number of Questions Solved	18
Category	NCERT Solutions

NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Ex 10.3

Question 1.
Find the angle between two vectors with magnitudes √3 and 2 respectively, and such that
Solution:
Angle θ between two vectors ,

Question 2.
Find the angle between the vectors
Solution:
Let
Let θ be the angle between ,

Question 3.
Find the projection of the vector , on the line represented by the vector ,
Solution:
let

Question 4.
Find the projection of the vector on the vector
Solution:
let then

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

Question 6.

Solution:
Given

Question 7.
Evaluate the product :

Solution:

Question 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
Solution:
We know that

Question 9.
Find , if for a unit vector
Solution:
Given

Question 10.
If such that , then find the value of λ.
Solution:
Given

Question 11.
Show that for any two non-zero vectors
Solution:
are any two non zero vectors

Question 12.
If , then what can be concluded about the vector ?
Solution:
,
=> = 0
Hence b is any vector.

Question 13.
If are the unit vector such that , then find the value of
Solution:
We have

Question 14.
If either vector then . But the converse need not be true. Justify your answer with an example.
Solution:
Given:
To prove:

Question 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.
Solution:
Let O be the origin then.

Question 16.
Show that the points A (1,2,7), B (2,6,3) and C (3,10, -1) are collinear.
Solution:
The position vectors of points A, B, C are

Question 17.
Show that the vectors and from the vertices of a right angled triangle.
Solution:
The position vectors of the points A, B and C are
and

Question 18.
If is a non-zero vector of magnitude ‘a’ and λ is a non- zero scalar, then λ is unit vector if
(a) λ = 1
(b) λ = – 1
(c) a = |λ|
(d) a =
Solution:

Given : is a unit vectors

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