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Not necessarily. Two skew lines will not lie in the same plane.
For example, consider you are standing in a cuboid room facing a wall. Then think of line 1 = the line where the floor and opposite wall meet. Line 2 = the line where two other walls meet. These two lines are not in the same plane.
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When lines intersect at the same point are they on the same plane?
No because only co-linear lines lie on the same plane
Three lines that intersect in a point but do not all lie in the same plane?
collinear plane
Do skew lines intersect if they are in the same plane?
No, skew lines cannot be in the same plane, since they do not have a point on common. Two lines intersect if they lie in a common plane, and by definition, these intersecting lines are not skew lines.
Do three lines that intersect at the same point have to be at the same plane?
No they can be Collinear - Points that lie on the same line.
Will non parallel lines intersect?
If the 2 lines lie in the same plane, and they are not parallel, then they will intersect at some point. If the 2 lines are skew lines, then they are not in the same plane, and they will not intersect (but they are Not Parallel)
