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

If position vectors of the points A, B and C are a, b and c respectively and the points D and E divides line segment AC and AB in the ratio 2:1 and 1:3, respectively. Then, the points of intersection of BD and EC divides EC in the ratio

If veca=-2hati+3hatj+5hatk,vecb=hati+2hatj+3hatkandvecc=7hati-hatk are position vectors of three points A, B, C respectively, prove that A, B, C are collinear.

Let vec a and vec b be the position vectors of the points (3,-5) and (m,4) respectively. Find m if the vectors vec a and vec b are collinear.

Show that points A(-2,1),B(-5,-1) and C(1,3) are collinear.

Two circles intersect at A and and AC,AD are respectively the diameter of the circle . Prove that the points C,B and D are collinear.

Using vectors, prove that the point A(1,2), B(3,8) and (-3,-10) are collinear.

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

Prove that the points (a ,b+c),(b ,c+a)a n d(c ,a+b) are collinear.

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 prove that quadrilateral A B C D is a parallelogram.