How do I determine if 3 points fall on a straight line?

Question

$1.\;A(0,0,0),\,B(9,−4,3),\,C(−36,16,−12)\\ 2.\;D(9,−4,3),\,E(10,−2,6),\,F(14,6,18)\\ 3.\;G(−1,0,1),\,H(3,9,10),\,I(8,27,28)$

I want to determine if these points fall on a straight line.

From my method 1 does, but 2 and 3 don't. But I am not sure if I am doing it right. What I did is find AB, then BC and see that its the same slope.

Answer 1

Pick one point, say $A$ then form $B-A$, $C-A$ and check that they are multiples of each other.

I get $(C-A) = -4(B-A)$ so they are on a straight line.

I get $(F-D) = 5(E-D)$ so they are on a straight line.

$I-G$ is not a multiple of $H-G$ so they are not colinear.

Answer 2

Consider these three points as a triangle. What would be its area, if they are collinear?