Find $\mid\overrightarrow{x}\mid$,if for a unit vector $\overrightarrow{a},(\overrightarrow{x}-\overrightarrow{a}).(\overrightarrow{x}+\overrightarrow{a})=15.$

Question

This question appeared in 65-1,65-2 and 65-3 versions of the paper in 2013.