Question:
Find the equation of a line in vector and cartesian form which passes through the point \((1,2,-4)\) and is perpendicular to the lines \(\frac{x-8}{3}=\frac{y+19}{-16}=\frac{z-10}{7}\) and \(\vec{r}=15\hat{i}+29\hat{j}+5\hat{k}+\mu(3\hat{i}+8\hat{j}-5\hat{k}).\)