Finding sets of points that lie on a straight line?

Question

its in 3D (Calculus)...how do you figure out if:

A(1,4,1) B(11,9,6) C(9,85) actually lies on a straight line.

what formula do you use and how do you break this problem down?

Answer 1

Okay, one way is finding x such that

x(11-1,9-4,6-1) = (11-9,9-8,6-5), or

(10x,5x,5x)=(2,1,1).

So, 10x=2, so x=2/10=1/5.

And as you can see,

((10(1/5)), 5(1/5), 5(1/5))) =

(2,1,1).

So, they lie on a straight line.