RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.4

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