Let \[\overrightarrow{A}={{a}_{1}}\hat{i}+{{a}_{2}}\hat{j}+{{a}_{3}}\hat{k},\text{ }\overrightarrow{B}={{b}_{1}}\hat{i}+{{b}_{2}}\hat{j}+{{b}_{3}}\hat{k}\] and \[\overrightarrow{C}={{c}_{1}}\hat{i}+{{c}_{2}}\hat{j}+{{c}_{3}}\hat{k}\] be three non-zero vectors such that \[\overrightarrow{C}\] is a unit vector perpendicular to both the vectors \[\overrightarrow{A}\] and \[\overrightarrow{B}\] .If the angle between \[\overrightarrow{A}\] and \[\overrightarrow{B}\] is \[\frac{\pi }{6}\], then.

• A. 0
• B. 1
• C. \[\frac{1}{4}(a_{1}^{2}+a_{2}^{2}+a_{3}^{2})(b_{1}^{2}+b_{3}^{2})\]
• D. \[\frac{3}{4}(a_{1}^{2}+a_{2}^{2}+a_{3}^{2})(b_{1}^{2}+b_{2}^{2}+b_{3}^{2})(c_{1}^{2}+c_{3}^{2})\]