[Math] Do these three points lie in the same plane $\mathbb{R}^{3}$

Question

$(1,0,0), (1,0,0), (0,0,0)$

I read that they lie in the same plane when they are different?
But It wasn't said how different they need to be. All of them need to be different from one another? In this example I wouldn't be sure because only two of them are not different. But I would say they do not lie in the same plane.

Answer 1

Any plane though the $x$ axis includes both of the two points. The fact that you list one point twice does not change the fact that there are only two distinct points in the list.