Give an example of three different points in $\mathbb R^3$ such that there are infinitely many planes in $\mathbb R^3$ passing through all of them.

Question

A past exam question. I'm not certain on the meaning.

I assume it wants a $3$ points on a straight line, one which case there would be infinitely many planes passing through all of them. But that seems too easy as you could make up any straight line equation and find $3$ points which fit it.

Do you have an alternative interpretation?

Note: $\mathbb R^3$ is the vector space.

Answer 1

you'll get infinitely many planes if and only if they lie on a straight line. It is commonly said that "3 points define a plane" but this is true only if they aren't on a straight line.