The two adjacent sides of a parallelogram are represented by vectors $2\hat{i}-4\hat{j}+$ $5\hat{k}$ and $\hat{i}-2\hat{j}-3\hat{k}$. Find the unit vector parallel to one of its diagonals. Also, find the area of the parallelogram.ORIf $\vec{a}=2\hat{i}+2\hat{j}+3\hat{k}, \vec{b}=-\hat{i}+2\hat{j}+\hat{k}$ and $\vec{c}=3\hat{i}+\hat{j}$ are such that the vector $(\vec{a}+\lambda\vec{b})$ is perpendicular to vector $\vec{c}$, then find the value of $\lambda$.