1). if  vector a, vector b ,vector c are the position vectors of the non- collinear points A,B,C resp. then show that a*b+b*c+c*a is perpendicular to the plane of ABC.(* is actually cross).,where a,b,c are vectors.

 

2). Let a ,b,c be 3 non zero vectors. if a.(b*c)=0 and b,c are not parallel then prove that a=b+kc  where  and k are some scalars.

 

3). if a,b,c represent the vectors BC,CA and AB of a triangle ABC then show that a*b=b*c=c*a.

(* is actually cross product in vectors in all 3 sums)