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

The point (a , b + c) , (b , c + a) and (c , a + b)

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

Prove that the (a, b+c), (b, c+a) and (c, a+b) are collinear.

Prove that the points A(a, 0), B(0, b) and C(1, 1) are collinear, if (1)/(a) + (1)/(b) = 1.

i. Prove that the points vec a-2vec b+3vec c, 2vec a+3vec b-4vec c and -7vecb+10 vec c are are collinear, where vec a, vec b, vec c are non-coplanar. ii. Prove that the points A(1,2,3), B(3,4,7), and C(-3,-2,-5) are collinear. find the ratio in which point C divides AB.

If a!=b!=c, prove that the points (a,a^(2)),(b,b^(2)),(c,c^(2)) can never be collinear.

The points (a,b+c),(b,c+a),(c,a+b) are

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