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Plane perpendicular to a line

Find plane α perpendicular to line r (direction (2, 1, 2)) through P(24, 14, 5).

Step-by-step solution

1. The normal of the plane perpendicular to r is the direction of r.
2. That normal and point P determine the plane.
3. Check that α₁ ⊥ r′ and α₂ ⊥ r″.

Result: α has normal (2, 1, 2) through P(24, 14, 5).

It is the same problem as the line perpendicular to the plane, seen the other way round.

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