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Q: Given any three points is there exactly one plane containing them?

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yes

It contains the whole line.

a straight line ..

No, 2 points define a line, 3 points define a plane.

No, two points define a line. It takes three points to define a plane.

Related questions

There are no planes containing any number of given points. Two points not the same define a line. Three points not in a line define a plane. For four or more points to lie in the same plane, three can be arbitrary but not on the same line, but the fourth (and so on) points must lie in that same plane.

a circle

They are points on the circumference of a unique circle in the plane.

If you are given a plane, you can always find and number of points that are not in that plane but, given anythree points there is always at least one plane that goes through all three.

The points are collinear, and there is an infinite number of planes that contain a given line. A plane containing the line can be rotated about the line by any number of degrees to form an unlimited number of other planes.If, on the other hand, the points are not collinear, then the plane has no wriggle room: it is stuck fast in one place - there can be only one plane containing all the points. Provided they are non-colinear, three points will define a plane.

No. The tiniest piece of a plane contains an infinite number of points. But if you give us just three points, then we know exactly what plane you're talking about, and it can't be any other plane.

If it is a straight line it must be in the same plane. Otherwise not necessarily.

Collinear points

yes

A circle is the set of all points in a plane at a given distance FROM a given point, which is known as the circle's center.

I think you mean: Are any three points contained in exactly one plane? only if they're not collinear... I think

false

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