UPSC NDA Math Model Paper 10

Let

→

b

=x

^

i

+y

^

j

+z

^

k

, Since b is collinear with vector a then

→

a

=λ

→

b

Where k is a scalar
Given

→

a

=(2,2,−3)
(2,2,−3)=k(x,y,z)
⇒x=

2

k

,y=

2

k

,z=

−3

k

Now,

→

a

.

→

b

=3
⇒ 2x + 2y - 3z = 3
⇒ 2/k + 2(2/k) - 3(-3/k) = 3
⇒ 2/k + 4/k + 9/k = 3
⇒ k = 5
So, x = 2/5, y = 2/5,and z = -3/5

→

b

= (2/5, 2/5, -3/5)
Hence, option (4) is correct.