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Intersection of two lines

Study the intersection of lines r (through P(3, 10, 8), direction (4, 4, 4)) and s (through Q(3, 10, 8), direction (4, 2, 3)).

Step-by-step solution

1. If the directions are parallel, the lines are parallel or coincident.
2. If not, check whether a common point exists by solving the system.
3. If there is no common point and they are not parallel, they are skew.
4. Check the result by substituting the point into both lines.

Result: they meet at I(3, 10, 8).

Two non-parallel lines can be skew without meeting: in dihedral, their projections cross but the crossing points are not on the same vertical.

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