Problem:
Point of intersection
Shows a cuboid OABCDEFG, where O is the origin. A has position vector 5i, C has position vector 10j and D has position vector 20k.
(a) Find the cosine of angle CAF.
Given that the point X lies on AC and that FX is perpendicular to AC,
(b) find the position vector of point X and the distance FX.
The line l1 passes through O and through the midpoint of the face ABFE. The line l2 passes through A and through the midpoint of the edge FG.
(c) Show that l2 and l2 intersect and find the coordinates of the point of intersection