how many planes are determinded by four noncoplanar points, exactly three of which are collinear?

Answer 1

4
They're all noncoplanar, so they must on a plane of their own. 4 points equal 4 planes.

Answer 2

The situation you describe is impossible. You cannot have 3 collinear points without them also being co-planer.

However, if you meant that all 4 points are not in the same plane, but, 3 of them are collinear, then you really have the same situation of 3 points non-collinear.

Imagine a plane containing the first line. The line acts like a hinge and the plane can swing around. Now, there will be only one place where that swinging plane hits the 4th point. Therefore, the modified situation I described still has only 1 solution and therefore only 1 plane.

Answer 3

Clearly you don't know what the words mean.

Non-coplanar means 'not in the same plane' which, for four points, cannot happen in 3 or 4 space.

Colinear means 'on the same line' and colinear in N space *always* implies coplaner in N+1 space.

If the question is embedded in 3 space, then the answer would be one plane.


Doug

Answer 4

One. Try to visualize it. Three noncolinear points determine a plane. You have to pick the one noncolinear point, and then you need two more. But it doesn't matter which two you pick from the three colinear ones.

Edit: woops, Doug is right. I read your question as "4 noncolinear points, three of which are colinear."