If the position vectors of the points A,B and C be a,b and 3a-2b respectively, then prove that the points A,B and C are collinear.

If the position vectors of the points A,B and C be hati+hatj,hati-hatj and ahati+bhatj+chatk respectively, then the points A,B and C are collinear, if

The position vectors of the points A, B, C are vec(a),vec(b) and vec( c ) respectively. If the points A, B, C are collinear then prove that vec(a)xx vec(b)+vec(b)xx vec( c )+vec( c )xxvec(a)=vec(0) .

The position vectors of the points (1, -1) and (-2, m) are vec(a) and vec(b) respectively. If vec(a) and vec(b) are collinear then find the value of m.

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.

Show that the points A(1,3,2),B(-2,0,1) and C(4,6,3) are collinear.

If the position vectors of the points A and B are hati+3hatj-hatk and 3hati-hatj-3hatk , then what will be the position vector of the mid-point of AB

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

If vec a , vec b , vec c , vec d are the position vector of point A , B , C and D , respectively referred to the same origin O such that no three of these point are collinear and vec a + vec c = vec b + vec d , than quadrilateral A B C D is a ;

Show that points A(a,b+c),B(b,c+a) and C(c,a+b) are collinear

The position vectors of four points P,Q,R annd S are 2a+4c,5a+ 3sqrt(3)b+4c,-2sqrt(3)b+c and 2a+c respectively, prove that PQ is parallel to RS.