Should distinct non-parallel line in $R^3$ have intersection point? True or False?
By Andrew Adams •
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True or False Question: Any two distinct non-parallel lines in $R^3$ must have an intersection point.
I think it is not true, but not sure how to prove that. If you know the solution, can you please help me out to find it?
$\endgroup$ 21 Answer
$\begingroup$Two non parallel straight lines in 3-space can either intersect or else, be skew.
When they intersect in a common plane, they have a common normal PZ to the plane at intersection point.
When skew like PY and black line through Q their common normal PQZ includes minimum distance between intersection points PQ.
If the straight lines are represented by vectors $(\bar X,\bar Y)$, then their common normal has direction of cross vector product $(\bar X \,\times \bar Y)$.
