# basic question.

• Jul 16th 2013, 01:53 PM
hisajesh
basic question.
They say, there is exactly one plane passing through three non collinear points. Does that mean each non collinear mentioned point has a plane?
• Jul 16th 2013, 02:33 PM
Plato
Re: basic question.
Quote:

Originally Posted by hisajesh
They say, there is exactly one plane passing through three non collinear points. Does that mean each non collinear mentioned point has a plane?

That you wrote make no sense whatsoever.

The statement means that for any set of three non collinear points there is a unique plane that has the given set as a subset.
• Jul 16th 2013, 03:39 PM
HallsofIvy
Re: basic question.
There exist an infinite number of planes through any ony point.

There exist an infinite number of points through any two points. (Rotating around the line through the two points)

There exist exactly one plane through any given three points. (Take those planes rotating around line through the two points and rotate until it touches that third point.)
• Jul 16th 2013, 04:08 PM
Soroban
Re: basic question.
Hello, hisajesh!

As Plato pointed out, your question is baffling.
Let's look at a simpler problem.

Quote:

They say: there is exactly one line passing through two distinct points.
Does that mean each distinct point has a line?

We are given two distinct points.

Code:

```             P *       Q *```

There is exactly one line through the two points.

Code:

```                /               /             P *             /             /           /           /         /       Q *       /       /```

You ask: Does each point have a line?

Answer: Um . . . yeah . . . I guess.

Code:

```                /               /             P *             /             /           /         /       Q *       /       /```