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MathGeometry

Find a Plane Containing a Line and Parallel to Another Line

Use two skew lines to find the plane containing the first and parallel to the second, then verify both conditions.

Question

The skew lines are L₁: x=t, y=t+2, z=3−t and L₂: x=s−1, y=2s−1, z=2s. Find an equation of a plane containing L₁ and parallel to L₂.

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Evidence boundary

Both line equations and their skew relationship come from the stated Millersville example. The answer applies to this version; a single line alone would leave infinitely many possible planes.