Three COLLINEAR points . . .
they determine a line.
An infinite number of different planes can also contain the line,
so the three collinear points don't nail down any specific plane.
Three NON-collinear points . . .
they determine one plane for sure, and only one.
That's why a three-legged stool or tripod is always stable and
doesn't wiggle. No matter how bumpy or rolling the floor or the
ground may be, the ends of the three legs determine exactly one
stable plane, so wherever they fall, they're standing on a stable plane.
The part on top where you sit is stable and doesn't wiggle.
