Read · 1 min
The exception is when all three points are collinear (this gives enough information to determine at most a line, if not a point).
When three points determine one plane, those points are said to be coplanar. Any set of collinear points is also coplanar too, though.
Two non-intersecting lines do not necessarily determine a plane because they may not be in the same plane. Such lines are called skew lines. Skew lines are neither parallel nor intersecting.
Interactive · 1 question
Which of these suffice(s) to uniquely determine a plane?
A set of points is collinear if they lie on the same line. Similarly, a set of points is coplanar if they lie on the same plane.
In general, any three noncollinear points suffice to determine a plane. Since any line contains two distinct points, having a line and a point not on the line also suffices to determine a plane. Having two distinct lines suffices as long as they actually share a plane, as is the case if they share a point or a direction.
Interactive · 1 question
We know that one point determines a point. We also know that two non-coinciding points determine a line.
Now what do 3 points form?
If the 3 points are not collinear, yes, they do form a triangle. But we need to extend this principle. They are not just stuck in that space, it is infinite. So, we just need 3 non-collinear points to form a .
