Line perpendicular to another through a point

Through P(17, 11, 7) draw line s perpendicular to r, which passes through A(16, 10, 4) with direction (3, 1, 3).

Step-by-step solution

If r is parallel to a projection plane, the perpendicularity is seen in that view.
If not, draw through P the plane perpendicular to r and contain in it a line through P.
Check that the dot product of the directions is 0.

Result: s passes through P(17, 11, 7) with direction (-6, 6, 4).

There are infinitely many perpendiculars to r through P: all those lying in the plane perpendicular to r.