$ABCD$ is a tetrahedron with position vectors as $A(\hat{j}+2\hat{k})$, $B(3\hat{i}+\hat{k})$, $C(4\hat{i}+3\hat{j}+6\hat{k})$,$D(2\hat{i}+3\hat{j}+2\hat{k})$. We have to find the perpendicular distance between point $A$ and $BC$.
I can solve it by using coordinate geometry (not by vectors).
I want to know how can we solve it using vectors .
Here's a hint: assume you already have the normal vector to the plane. Can you say anything about the perpendicular distance now? You should be able to take it from here.