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NCERT Solutions for Maths Class 12 Exercise 10.1
NCERT Solutions for Maths Class 12 Exercise 10.3
NCERT Solutions for Maths Class 12 Exercise 10.4
NCERT Solutions for Maths Class
12 Exercise 10.2
Maths Class
12 Ex 10.2 Question 1.
Compute the magnitude of the following vectors:
Maths Class
12 Ex 10.2 Question 2.
Write two different vectors having same magnitude.
Solution:
Maths Class
12 Ex 10.2 Question 3.
Write two different vectors having same direction.
Solution:
Let the two vectors are:
Hence, vectors
Maths Class
12 Ex 10.2 Question 4.
Find the values of x and
y so that the vectors 
We are given
If vectors are equal, then their respective components are also equal.
On comparing the components in both the vectors, we get x = 2, y = 3.
Maths Class
12 Ex 10.2 Question 5.
Find the scalar and vector components of the vector with initial
point (2, 1) and terminal point (–5, 7).
Solution:
Let A (2, 1) be the initial point and B (–5, 7) be the terminal
point.
Maths Class
12 Ex 10.2 Question 6.
Find the sum of the vectors
Solution:
We have,
Thus, the sum of the vectors is
Maths Class 12 Ex 10.2 Question 7.
Find the unit vector in the direction of the vector 
Solution:
We are given that
Maths Class 12 Ex 10.2 Question 8.
Find the unit vector in the direction of vector 
Solution:
The points P and Q are (1, 2, 3) and (4, 5, 6), respectively.
For given vectors, 
Solution:
We are given that
Maths Class 12 Ex 10.2 Question 10.
Find a vector in the direction of vector 
Solution:
Let the given vector is
Show that the vectors 
Solution:
Let the given vectors
are
Maths Class
12 Ex 10.2 Question 12.
Find the direction cosines of the vector 
Solution:
Let
Here, a = 1, b = 2, c = 3
Find the direction cosines of the vector joining the points A (1, 2,
–3) and B (–1, –2, 1), directed from A to B.
Solution:
Vector joining the points A and B is
Maths Class
12 Ex 10.2 Question 14.
Show that the vector 
Solution:
Let 
This shows that the given vector is equally inclined to the axes OX, OY, OZ.
Find the position vector of a point R which divides the line
joining two points P and Q whose position vectors are 
(i) internally
(ii) externally.
Solution:
(i) The point R which divides the line joining the points
Find the position vector of the midpoint of the vector joining the
points P (2, 3, 4) and Q (4, 1, –2).
Solution:
Maths Class
12 Ex 10.2 Question 17.
Show that the points A, B and C with position vectors, 
Solution:
In triangle ABC (figure), which of the following is not true:
Solution:
Using vectors law, we have
Hence, the correct answer is option (C).
Maths Class
12 Ex 10.2 Question 19.
If 
(A) 
(B)
(C) the respective components of
(D) both the vectors
Solution:
Since both the vectors
Hence, the correct answer is option (D).
Related Links:
NCERT Solutions for Maths Class 12 Exercise 10.1