# RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.3

## Rajasthan Board RBSE Class 12 Maths Chapter 13 Vector Ex 13.3

RBSE Solutions For Class 12 Maths Chapter 13.3 Question 1.
Find vector product of vectors

and

Solution:

RBSE Solutions For Class 12 Maths Chapter 13 Question 2.
Find perpendicular unit vector of vectors

and

Solution:

Exercise 13.3 Class 12 RBSE Question 3.
For vectors $$\overrightarrow { a }$$ and $$\overrightarrow { b }$$, prove that

Solution:

Ex 13.3 Class 12 RBSE Question 4.
Prove that

Solution:
According to question,

RBSE Class 12 Maths Chapter 13 Question 5.
If $$\overrightarrow { a }$$, $$\overrightarrow { b }$$, $$\overrightarrow { c }$$ are unit vectors, such that
$$\overrightarrow { a }$$ . $$\overrightarrow { b }$$ = 0 = $$\overrightarrow { a }$$ . $$\overrightarrow { c }$$ and angle between $$\overrightarrow { b }$$ and $$\overrightarrow { c }$$ is $$\frac { \pi }{ 6 }$$, then prove that $$\overrightarrow { a }$$ = ± 2 ($$\overrightarrow { b }$$ × $$\overrightarrow { c }$$)
Solution:
Given that

Maths Class 12 Exercise 13.3 Question 6.
Find the value of

Solution:
We know that if $$\overrightarrow { a }$$ and $$\overrightarrow { b }$$ are two vectors and θ is the angle between them, then

Exercise 13.3class 12 Question 7.
Find vector perpendicular to the vectors

and

whose magnitude is 9 unit.
Solution:

Class 9 Math Exercise 13.3 Question 8.
Show that:

also, explain geometrically.
Solution:

= 2(vector area of parallelogram ABCD).
Thus we conclude that area of parallelogram whose adjacent sides are diagonals of given parallelogram is twice the area of given parallellogram.

Ex 13.3 Class 12 Question 9.
For any vector $$\overrightarrow { a }$$, prove that

Solution:

Ex 13.3 Class 10 Question 10.
If two adjacent sides of a triangle are represented by vectors

and

then find the area of triangle.
Solution: