# RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.1

## Rajasthan Board RBSE Class 12 Maths Chapter 13 Vector Ex 13.1

RBSE Solutions For Class 12 Maths Chapter 13 Question 1.
Compute the magnitude of the following vectors :

Solution:

RBSE Solutions For Class 12 Maths Chapter 13.1 Question 2.
Write two different vectors having same magnitude.
Solution:

RBSE Class 12 Maths Chapter 13 Question 3.
Write two different vectors having same direction.
Solution:

Exercise 13.1 Class 12 Question 4.
Find the values of x and y so that the vectors 2 $$\widehat { i }$$ + 3 $$\widehat { j }$$ and x $$\widehat { i }$$ + y $$\widehat { j }$$ are equal.
Solution:
Two vectors are equal if their corresponding coefficients are equal

⇒ 2 = x and 3 = y
x = 2 and y = 3.

12 Maths RBSE Solution Question 5.
Find the scalar and vector components of the vector with initial point (2,1) and terminal point (- 5,7).
Solution:
Coordinates of initial point A are (2, 1).
and coordinates of terminal point B are (- 5, 7)
Now from formula

Ex 13.1 Class 10 RBSE Question 6.

Solution:

12th Maths RBSE Solution Question 7.
Find the unit vector in the direction of the vector $$\widehat { a }$$ = $$\widehat { i }$$ + $$\widehat { j }$$ + 2 $$\widehat { k }$$
Solution:

RBSE Solution Class 12 Maths Question 8.
Find the unit vector in the direction of vector $$\overrightarrow { PQ }$$ where P and Q are the points (1,2,3) and (4,5,6).
Solution:

RBSE Solutions For Class 10 Maths Chapter 13.1 Question 9.
For the given vectors,

and

Find the unit vector in the direction of the vector $$\overrightarrow { a } +\overrightarrow { b }$$
Solution:

Class 12 Chapter 13 Exercise 13.1 Question 10.
Find a vector in the direction of vector

which has magnitude 8 units.
Solution:

Class 12 Maths Chapter 13 Exercise 13.1 Question 11.
Show that the vectors

and are collinear.

Solution:

Maths Class 12 RBSE Question 12.
Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are

and

respectively in the ratio 2:1.
(i) internally (ii) externally.
Solution:

Ch 13 Maths Class 12 Question 13.
Find the position vector of the midpoint of the vector joining the points P(2,3,4) and Q(4, 1, -2).
Solution:

Class 12 Maths RBSE Solutions Question 14.
Show that the points A, B and C with position vectors,

and

respectively from the vertices of a right angled triangle.
Solution:
Let O is the origin, then according to question,

Hence ∆ABC is a right angled triangle,
or point A, B and C are the vertices of a right angled triangle.