Assignment:
Figure 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 l1 and l2 intersect and find the coordinates of the point of intersection.
Provide complete and step by step solution for the question and show calculations and use formulas.