## 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: