Let a, b be unit vectors. If c be a vector such that the angle between a and c is (π)/12, and b = c +2( c × a ), then |6 c |^2 is equal to:

Let $\displaystyle \hat{\mathrm{a}}, \hat{\mathrm{b}}$ be unit vectors. If $\displaystyle \overrightarrow{\mathrm{c}}$ be a vector such that the angle between $\displaystyle \hat{\mathrm{a}}$ and $\displaystyle \overrightarrow{\mathrm{c}}$ is $\displaystyle \frac{\pi}{12}$, and $\displaystyle \hat{\mathrm{b}}=\overrightarrow{\mathrm{c}}+2(\overrightarrow{\mathrm{c}} \times \hat{\mathrm{a}})$, then $\displaystyle |6 \overrightarrow{\mathrm{c}}|^2$ is equal to :