Let a = a_1 i + a_2 j + a_3 k and b = b_1 i + b_2 j + b_3 k be two vectors such that | a |=1, a · b =2 and | b |=4. If c =2( a × b )-3 b, then the…

Let $\displaystyle \overrightarrow{\mathrm{a}}=\mathrm{a}_1 \hat{i}+\mathrm{a}_2 \hat{j}+\mathrm{a}_3 \hat{k}$ and $\displaystyle \overrightarrow{\mathrm{b}}=\mathrm{b}_1 \hat{i}+\mathrm{b}_2 \hat{j}+\mathrm{b}_3 \hat{k}$ be two vectors such that $\displaystyle |\overrightarrow{\mathrm{a}}|=1$, $\displaystyle \overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{b}}=2$ and $\displaystyle |\overrightarrow{\mathrm{b}}|=4$. If $\displaystyle \overrightarrow{\mathrm{c}}=2(\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}})-3 \overrightarrow{\mathrm{~b}}$, then the angle between $\displaystyle \overrightarrow{\mathrm{b}}$ and $\displaystyle \overrightarrow{\mathrm{c}}$ is equal to: