## Rajasthan Board RBSE Class 12 Maths Chapter 13 Vector Ex 13.2

**RBSE Solutions For Class 12 Maths Chapter 13.2 Question 1.**

If magnitude of two vectors be 4 and 5 units, then find scalar product of them, where angle between them be :

(i) 60°

(ii) 90°

(iii) 30°

Solution:

**RBSE Solutions For Class 12 Maths Chapter 13 Question 2.**

Find \(\overrightarrow { a } \). \(\overrightarrow { b } \) , if \(\overrightarrow { a } \) and \(\overrightarrow { b } \) are as follow :

Solution:

**Exercise 13.2 Class 12 RBSE Question 3.**

Prove that:

Solution:

**RBSE Class 12 Maths Chapter 13 Question 4.**

If coordinates of P and Q are (3, 4) and (12, 4) respectively, then find ∠POQ where O is origin.

Solution:

**Exercise 13.2 Class 12 Question 5.**

For which value of λ, vectors \(\overrightarrow { a } \) and \(\overrightarrow { b } \) are mutually perpendicular :

Solution:

**Maths RBSE Solutions Class 12 Question 6.**

Find the projection of the vector

on the vector

Solution:

**12th Class RBSE Solution Question 7.**

If

and

then find a vector \(\overrightarrow { c } \), so that \(\overrightarrow { a } \), \(\overrightarrow { b } \), \(\overrightarrow { c } \) represents the sides of a right angled triangle.

Solution:

Given that

**RBSE Solution 12th Class Question 8.**

If | \(\overrightarrow { a } \) + \(\overrightarrow { b } \) | = | \(\overrightarrow { a } \) – \(\overrightarrow { b } \) |, then prove that \(\overrightarrow { a } \) and \(\overrightarrow { b } \) are mutually perpendicular vectors.

Solution:

According to question,

**RBSE Solution Class 12th English Question 9.**

If coordinates of points A, B, C and D are (3, 2, 4), (4, 5, -1), (6, 3, 2) and (2, 1, 0) respectively, then prove that lines \(\overrightarrow { AB } \) and \(\overrightarrow { CD } \) are mutually erpendicular.

Solution:

Given that coordinates of points A, B, C and D are (3,2,4), (4,5,-1), (6,3,2) and (2,1,0) respectively.

Then position vectors of A, B, C and D with respect to origin are

**RBSE Solution Class 12th Maths Question 10.**

For any vector \(\overrightarrow { a } \), prove that

Solution:

**RBSE Solutions Of Class 12 Question 11.**

Use vectors to prove that sum of square of diagonal of a parallelogram is equal to the sum of square of their side.

Solution:

Let OACB is a parallelogram. Taking O as origin, the position vectors of A and B are \(\overrightarrow { a } \) and \(\overrightarrow { b } \) respectively.

∴ Sum of the squares of diagonals = sum of the squares of sides.

Hence the sum of square of diagonals of a parallelogram is equal to the sum of square of their sides.