(a) Let $\vec{a}=\hat{i}+\hat{j}, \vec{b}=\hat{i}-\hat{j}$ and $\vec{c}=\hat{i}+\hat{j}+\hat{k}$. If $\hat{n}$ is a unit vector such that $\vec{a} \cdot \hat{n}=0$ and $\vec{b} \cdot \hat{n}=0$, then find $\left| \vec{c} \cdot \hat{n} \right|$ OR (b) If $\vec{a}$ and $\vec{b}$ are unit vectors inclined at an angle $30^{\circ}$ to each other, then find the area of the parallelogram with $(\vec{a}+3\vec{b})$ and $(3\vec{a}+\vec{b})$ as adjacent sides.