How do 3 non-collinear points provide stability for an object?

Question

I know that 3 non-collinear points form a unique plane. However, I have a hard understanding why a unique plane would provide stability for an object (eg. a stool with 3 legs). Could someone explain this?

Thanks everybody!

Answer 1

If you think about why a table is unstable it is because one of the legs is too short. When someone leans on the table it pivots about the line defined by the ends of two of the legs and settles into a new plane. This cannot happen if there are only three legs because there is only one plane into which the table can settle.

Answer 2

No matter what the lengths of the legs, there is a unique plane that they lie in. This means that, when placed on the ground, the table will be stable.

Also, if the lengths of the legs are about the same, then the top of the table will be close to horizontal.