Is one plane always passing through 3 noncolinear points.?

Answer 1

A plane is described as a surface that runs through any three points: that is the definition. If the points are collinear then they are on the same line and so the plane can be rotated around that combined axis in the third dimension thus creating a new plane.

A point at 1,1,1 along with a point at 3, 4, 1 and a third point at 6, 9, 1 would describe a plane with the same Z axis, since all points are collinear. If the second point was 2,2,2 then the plane would be inclined at an angle of 45 degrees in the z axis if the last point was at 4,4,4. But, since it is not a totally new plane is created independent of the original X, Y, and Z axis.

You can select any three unique points and create a plane between them. If you have less than 3 points then you only have created a plane on the X, Y axis, not the Z axis. If you have more than 3 points then the may not be coplanar. A plane described as 1,1, 1 to 2,2,1 to 3,3,1 would not contain the point 10,14,16. The last point is totally off the same Z axis of 1,1 and it isn't in the same axis if that runs from 1,1 to 3,3; the fourth point destroys your plane and creates a new rectangular like shape.

Answer 2

Yes. 3 non-collinear points *defines* a plane.