3d version of previous post by Hartlw is wrong.
Determine r0 = a + λ0c where line from B intersects given line perpendicularly:
(r0 - b)∙c = 0 → (a + λ0c – b).c = 0, determines λ0
r’ = b + λ’(r0 – b)
Sorry about that. In a way I’m glad, because previous solution (wrong) was almost impossible to visualize.