If A(4,8,12), B(2,4,6), C(3,5,4) and D(5,8,5) are four points, show that the lines `vec(AB) and vec(CD)` intersect.

If A(3, 4, 5), B(4, 6, 3), C(-1, 2, 4) and D(1, 0, 5) are such that the angle between the lines bar(DC) " and "bar(AB) " is " theta " then " costheta=

If P(2,3,-6) , Q (3, -4,5) are two points, find the d.c's of vec(OP), vec(QO) and vec(PQ) where O is the origin.

If A (4, 3, 5), B (6, 4, 3), C (2, -1, 4), D (0, 1, 5) then the projection of bar(AB) " on " bar(CD) is

A (-1,2-3), B(5,0,-6), C(0,4,-1) are three points, Show that direction cosines of the bisectors of lfloorBAC are proportional to (25,8,5)and (-11,20,23).