Show that the found points `A ,B ,C ,D` with position vectors ` vec a , vec b , vec c , vec d` respectively such that 3 ` vec a-2 vec b+5 vec c-6 vec d= vec0` , are coplanar. Also, find the position vector of the point of intersection of the line segments `A C` and `B Ddot`

Answer

`(3vec(a)+5vec(c ))/(8)` or `(2vec(b)+6vec(d))/(8)`.