Vector Algebra

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