If a unit vector is represented by 0.5 i + 0.8 j + ck, then find the value of c.

(a) 0.1

(b) √0.11

(c) √0.8

(d) 1

Solution:

Let vector a = 0.5 i + 0.8 j + ck

Since a is a unit vector, |a| = 1

=> 0.52+0.82+c2 = 1

O.25 + 0.64 + c2 = 1

So c2 = 1 – 0.64 – 0.25

= 0.11

Therefore c = √0.11

Hence option b is the answer.