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

If 4hati+5hatj+hatk,-(hatj+hatk),3hati+9hatj+4hatk and 4(-hati+hatj+hatk) are position vectors of the points A, B, C and D then prove that A, B, C, D are coplannar.

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.

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

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

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

Prove that the points hati-hatj,4hati+3hatj+hatk and 2hati-4hatj+5hatk are vertices of a right angled triangle.

Show that the points A(-2hati+3hatj+5hatk),B(hati+2hatj+3hatk)andC(7hati-hatk) are collinear.