## 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.