RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.4

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

RBSE Solutions for Class 12 Maths