# RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5

## Rajasthan Board RBSE Class 12 Maths Chapter 13 Vector Ex 13.5

Question 1.
Find the value of

Solution:

Question 2.
Prove that

Solution:

Question 3.
Evaluate the formula

Solution:

Question 4.
For any vector $$\overrightarrow { a }$$, prove that:

Solution:
We know that

Question 5.
Prove that

Solution:

Question 6.
Prove that $$\overrightarrow { a }$$,$$\overrightarrow { b }$$,$$\overrightarrow { c }$$ are coplanar if $$\overrightarrow { a }$$ × $$\overrightarrow { b }$$, $$\overrightarrow { b }$$ × $$\overrightarrow { c }$$, $$\overrightarrow { c }$$ × [/latex], $$\overrightarrow { a }$$ are coplanar
Solution:

Question 7.
Prove that

Solution:

Question 8.
If magnitude of two $$\overrightarrow { a }$$ and $$\overrightarrow { b }$$ are √3 and 2 respectively $$\overrightarrow { a }$$ and. $$\overrightarrow { b }$$ = √6, then find the angle between $$\overrightarrow { a }$$ and $$\overrightarrow { b }$$
Solution:

Question 9.
Find the angle between the vectors

and

Solution:

Question 10.
Find the projection of vector

Solution:

Question 11.
Find projection vector on vector

on vector

Solution:

Question 12.
Find the value of

Solution:

Question 13.
Find the magnitude of two vectors $$\overrightarrow { a }$$ and $$\overrightarrow { b }$$, if their magnitude are equal and angle between them is 60° and their scalar product is $$\frac { 1 }{ 2 }$$
Solution:
According to question

Question 14.
If for a vector $$\overrightarrow { a }$$, ($$\overrightarrow { x }$$ – $$\overrightarrow { a }$$ ).( $$\overrightarrow { x }$$ + $$\overrightarrow { a }$$ ) = 12, then | $$\overrightarrow { x }$$ |.
Solution:
According to question,

Question 15.

such that $$\overrightarrow { a }$$ + λ $$\overrightarrow { b }$$ is perpendicular on $$\overrightarrow { c }$$, then find the value of λ.
Solution:
According to question $$\overrightarrow { a }$$ + λ $$\overrightarrow { b }$$ is a perpendicular to $$\overrightarrow { c }$$

Question 16.
If vertices $$\overrightarrow { a }$$, $$\overrightarrow { b }$$, $$\overrightarrow { c }$$ are such that
$$\overrightarrow { a }$$ + $$\overrightarrow { b }$$ + $$\overrightarrow { c }$$ = $$\overrightarrow { 0 }$$
then, find the value of $$\overrightarrow { a }$$ . $$\overrightarrow { b }$$ + $$\overrightarrow { b }$$ . $$\overrightarrow { c }$$ + $$\overrightarrow { c }$$ . $$\overrightarrow { a }$$
Solution:
According to question

Question 17.
If vectors/1, B, C of triangle ABC are (1, 2,3), (-1,0, 0,), (0, 1, 2) respectively, then find ∠ABC.
Solution:
Let O be the origin.