Question:
Find the Cartesian and vector equations of the line passing through the point $(1,2,-4)$ and perpendicular to each of the lines $\frac{x-8}{8}=\frac{y+19}{-16}=\frac{z-10}{7}$ and $\frac{x-15}{3}=\frac{y+29}{8}=\frac{z-5}{-5}$.
Solution:
