the definition of intersecting lines is: two lines that meet and cross at the same at the same place
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Two lines that intersect and form a right angle.
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.
Parallel lines do not intersect.
Two lines cross or intersect at a point.
When two lines intersect they form an axes.