If the equation of the line passing through the point $\left(0,-\frac{1}{2}, 0\right)$ and perpendicular to the lines $\overrightarrow{\mathrm{r}}=\lambda(\hat{i}+\mathrm{a} \hat{j}+\mathrm{b} \hat{k}) \quad$ and $\quad \overrightarrow{\mathrm{r}}=(\hat{i}-\hat{j}-6 \hat{k})+\mu(-\mathrm{b} \hat{i}+\mathrm{a} \hat{j}+5 \hat{k}) \quad$ is $\quad \frac{x-1}{-2}=\frac{y+4}{\mathrm{~d}}=\frac{z-\mathrm{c}}{-4}$, then $\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}$ is equal to: