If $\overrightarrow{\mathit{a}}=\hat{\mathit{i}}+2\hat{\mathit{j}}+3\hat{\mathit{k}}$ and $\overrightarrow{\mathit{b}}=2\hat{\mathit{i}}+4\hat{\mathit{j}}-5\hat{\mathit{k}}$ represent two adjacent sides of a parallelogram, find unit vectors parallel to the diagonals of the parallelogram.
OR
Using vectors, find the area of the triangle $\mathrm{ABC}$ with vertices $\mathrm{A}\left(1,2,3\right)$, $\mathrm{B}\left(2,-1,4\right)$ and $\mathrm{C}\left(4,5,-1\right)$.