If `hati+hatj+hatk,2hati+5hatj,3hati+2hatj-3hatkandhati-6hatj-hatk` are position vectors of points A,B,C and D respectively , then find the angle between `vec(AB)andvec(CD)`. Deduce that `vec(AB)andvec(CD)` are collinear.

If a=3hati-2hatj+hatk,b=2hati-4hatj-3hatk and c=-hati+2hatj+2hatk , then a+b+c is

Show that the vectors 2hati-3hatj+4hatk and -4hati+6hatj-8hatk are collinear.

If the position vectors of A and B respectively hati+3hatj-7hatk and 5 hati-2hatj+4hatk , then find vec(AB)

If the vectors 6hati-2hatj+3hatk, 2hati+3hatj-6hatk and 3hati+6hatj-2hatk form a triangle, then it is

Show that the vectors hati-hatj-hatk,2hati+3hatj+hatk and 7hati+3hatj-4hatk are coplanar.

If a=hati+2hatj+3hatk,b=-hati+2hatj+hatk and c=3hati+hatj , then the unit vector along its resultant is

If 4hati+ 7hatj+ 8hatk, 2hati+ 3hatj+ 4hatk and 2hati+ 5hatj+7hatk are the position vectors of the vertices A, B and C, respectively, of triangle ABC, then the position vector of the point where the bisector of angle A meets BC is

If the vectors 4hati+11hatj+mhatk,7hati+2hatj+6hatk and hati+5hatj+4hatk are complanar then m=

If the vectors 2hati-hatj+hatk,hati+2hatj-3hatk and 3hati+ahatj+5hatk are coplanar, the prove that a=-4.

If position vector of points A,B and C are respectively hati,hatj, and hatk and AB=CX , then position vector of point X is