The unit vector parallel to the resultant vector $2\hat{i}+4\hat{\mathbf{j}}-5\hat{k}$ and $\hat{\mathbf{i}}+2\hat{\mathbf{j}}+3\hat{\mathbf{k}}$ is:

Resultant vector $\mathbf{r}=(2\mathbf{i}+4\mathbf{j}-5\mathbf{k})+(\mathbf{i}+2\mathbf{j}+3\mathbf{k})$

$=3\mathbf{i}+6\mathbf{j}-2\mathbf{k}$

Unit vector parallel to $\overline{\mathbf{r}}=\frac{1}{\left|\mathbf{r}\right|}\overline{\mathbf{r}}$

$=\frac{1}{\sqrt{3^2+6^2+(-2{)}^2}}(3\mathbf{i}+6\mathbf{j}-2\mathbf{k})=\frac{1}{7}(3\mathbf{i}+6\mathbf{j}-2\mathbf{k})$