Question:
Find the vector equation of a line passing through the point $(2 \hat{i}-3 \hat{j}-5 \hat{k})$ and perpendicular to the plane $\vec{r} \cdot(6 \hat{i}-3 \hat{j}+5 \hat{k})+2-0$.
Also, find the point of intersection of this line and the plane.
Solution:
