(a) Let $\overrightarrow{\mathit{a}}=\hat{\mathit{i}}+\hat{\mathit{j}},\overrightarrow{\mathit{b}}=\hat{\mathit{i}}-\hat{\mathit{j}}$ and $\overrightarrow{\mathit{c}}=\hat{\mathit{i}}+\hat{\mathit{j}}+\hat{\mathit{k}}$. If $\hat{\mathit{n}}$ is a unit vector such that $\overrightarrow{\mathit{a}}\cdot \hat{\mathit{n}}=0$ and $\overrightarrow{\mathit{b}}.\hat{\mathit{n}}=0$, then find $\mid \overrightarrow{\mathit{c}}\cdot \hat{\mathit{n}}|$

OR
(b) If $\overrightarrow{\mathit{a}}$ and $\overrightarrow{\mathit{b}}$ are unit vectors inclined at an angle ${30}^{\circ }$ to each other, then find the area of the parallelogram with $\left(\overrightarrow{\mathit{a}}+3\overrightarrow{\mathit{b}}\right)$ and $\left(3\overrightarrow{\mathit{a}}+\overrightarrow{\mathit{b}}\right)$ as adjacent sides.