Let a and b be two unit vectors such that | a + b |=√ 3. If c = a +2 b +3( a × b ), then 2| c | is equal to:

Let $\displaystyle \vec{a}$ and $\displaystyle \vec{b}$ be two unit vectors such that $\displaystyle |\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}|=\sqrt{3}$. If $\displaystyle \overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{a}}+2 \overrightarrow{\mathrm{~b}}+3(\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}})$, then $\displaystyle 2|\overrightarrow{\mathrm{c}}|$ is equal to :