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=\(\sqrt{0.11}\)