## Rajasthan Board RBSE Class 12 Maths Chapter 13 Vector Ex 13.4

Question 1.

Prove that:

Solution:

Question 2.

Solution:

Question 3.

Prove that vectors

and

are coplanar

Solution:

Question 4.

For which value of λ, following vectors are coplanar :

Solution:

Question 5.

Prove that the following four points are coplanar:

(i) A(- 1,4,-3), B(3,2,-5), C(- 3,8,-5), D(- 3,2,1)

(ii) A(0,-1,0), B(2,1,-1), C(1,1,1), D(3,30)

Solution:

(i) Given points are A(-1,4,-3), B(3,2,-5), C(- 3,8,-5) and D(-3,2,1)

Question 6.

Prove that

and

are vector sides of right angled triangle.

Solution:

Given sides are

Question 7.

Find the volume of parallelopiped, whose coterminous edges are given by following vectors :

Solution:

(i) The coterminous edges are

(ii) The coterminous edges are