Hello Students. In this post, you will find the complete NCERT Solutions for Maths Class 12 Exercise 10.3.
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NCERT Solutions for Maths Class 12 Exercise 10.1
NCERT Solutions for Maths Class 12 Exercise 10.2
NCERT Solutions for Maths Class 12 Exercise 10.4
NCERT Solutions for Maths Class 12 Exercise 10.3
Maths Class
12 Ex 10.3 Question 1.
Find the angle between two vectors a and b with magnitudes √3 and
2, respectively, having a . b = √6.
Solution:
Let θ be the angle between two vectors.
Given that a = √3, b = 2 and a . b
= √6
Maths Class
12 Ex 10.3 Question 2.
Find the angle between the vectors
Solution:
Let
Let θ be the angle between a and b.
Find the projection of the vector i – j on the vector i + j.
Solution:
Maths Class 12 Ex 10.3 Question 4.
Find the projection of the vector i + 3j + 7k on the vector 7i
– j + 8k.
Solution:
Maths Class
12 Ex 10.3 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:
Maths Class 12 Ex 10.3 Question 7.
Evaluate the product:
Solution:
Find the magnitude of two vectors a and b, having the same magnitude
and such that the angle between them is 60° and their scalar product is ½.
Solution:
We have given that, |a| = |b|, θ = 60˚ and a.b
= ½
We know that
Maths Class
12 Ex 10.3 Question 9.
Find |x|, if for a unit
vector
Solution:
Given that, a is a unit vector, then |a|
= 1.
If a = 2i + 2j + 3k, b = -i + 2j + k and c
= 3i
+ j
are such that a + λb is
perpendicular to c, then find the value of λ.
Solution:
Maths Class 12 Ex 10.3 Question 11.
Show that |a|b + |b|a is perpendicular to |a|b
– |b|a, for
any two non-zero vectors a and b.
Solution:
Maths Class 12 Ex 10.3 Question 12.
If 
Solution:
It is given that,
This implies that, b = 0
Hence, b is any vector.
Maths Class
12 Ex 10.3 Question 13.
If
Solution:
Maths Class 12 Ex 10.3 Question 14.
If either vector
Solution:
Maths Class 12 Ex 10.3 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.
[∠ABC is the angle between the
vectors BA and BC.]
Solution:
Maths Class 12 Ex 10.3 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 and C are:
Maths Class
12 Ex 10.3 Question 17.
Show that the vectors
Solution:
The position vectors of the points A, B and C are:
If a is
a non-zero vector of magnitude ‘a’
and λ is a non-zero scalar, then λa is unit vector if
(A) λ = 1
(B) λ = – 1
(C) a = |λ|
(D) a = 1/|λ|
Solution:
Hence, the correct answer is option (D).
Related Links:
NCERT Solutions for Maths Class 12 Exercise 10.1