Lines and planes - general concepts I've come across a book that has this general questions about lines and planes. I can't agree with some of the answers it presents, for the reasons that I'll state below: True or False: > * Three distinct points form a plane - BOOK ANSWER: True - MY ANSWER: False, they cannot belong to the same line > > * Two intersecting lines form a plane - BOOK ANSWER: True - MY ANSWER: False, they can be parallel and coincident lines. > > * Two lines that don't belong to a same plane are skew - BOOK ANSWER: True - MY ANSWER: True > > * If three lines are parallel, there is a plane that contains them - BOOK ANSWER: True - MY ANSWER: False, they can be parallel and coincident lines. > > * If three distinct lines are intersecting two by two, then they form only one plane - For this last one there's no answer and I'm not sure about the conclusion. > > If you could help me, I appreciate it. Thank you.

Assuming 3D Euclidean geometry:

* On point 1 if the three points are collinear there is more than one plane

* I would agree with the book and disagree with you on point 2 for a suitable definition of _intersecting_ (at exactly one point).

* I would disagree with the book on point 4 (consider the three parallel edges of a triangular prism).

* I would say True for point 5, again for a suitable definition of _intersecting two-by-two_ (the plane is defined by the three points of intersection, which do not lie on a single line and all three lines lie on it)