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