# RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.2

## 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.