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

Prove that the points (a, b), (c, d) and (a-c, b-d) are collinear, if ad = bc.

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

Show that points : A (a,b+c),B(b,c+a),C(c,a+b) 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.

The points with coordinates (2a,3a), (3b,2b) and (c,c) are collinear

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 a ne b ne c , prove that (a, a^2), (b, b^2), (c, c^2) can never be collinear.

Statement 1: if three points P ,Qa n dR have position vectors vec a , vec b ,a n d vec c , respectively, and 2 vec a+3 vec b-5 vec c=0, then the points P ,Q ,a n dR must be collinear. Statement 2: If for three points A ,B ,a n dC , vec A B=lambda vec A C , then points A ,B ,a n dC must be collinear.

Using determinants, show that the following points are collinear (a, b + c),(b,c+a) and (c, a + b)