Finding the intersection of an infinite ray with a plane in 3D is an important topic in collision detection.



Task

Find the point of intersection for the infinite ray with direction   (0, -1, -1)   passing through position   (0, 0, 10)   with the infinite plane with a normal vector of   (0, 0, 1)   and which passes through [0, 0, 5].




mp=: +/ .*                          NB. matrix product
p=: mp&{: %~ -~&{. mp {:@]          NB. solve
intersectLinePlane=: [ +/@:* 1 , p  NB. substitute