If a unit vector is represented by \(0.5\hat{i} +0.8\hat{ j} +c\hat{k} \) then the value of 'c' is

a)\(\sqrt{0.01}\)

b)\(\sqrt{0.11}\)

c)\(1\)

d)\(\sqrt{0.39}\)

Correct option is b) \(\sqrt{0.11}\)

Explaination::

The unit vector is given as \(\hat{A}=0.5\hat{i} +0.8\hat{ j} +c\hat{k}\)

Magnitude of unit vector is always equal to 1

\(\sqrt{(0.5)^2 +(0.8)^2 +(c)^2}=1\)

\(\therefore 0.25+0.64+c^2=1\)

c^{2}=1-0.89

c=\(\sqrt{0.11}\)