Two distinct points determine a line. When you have three distinct points, they *might* all be on the same line (in which case those points would be called "collinear"). So, do it for two points, then see if the 3rd point is also on that line.

So, pick two of those points (say (3, 0 0) and (0, 0, 3) since their the simpliest) and find the line between them. There are a few ways to do this. I prefer vectors.

Thus those three points are not collinear - there is no single line going through all three of them.