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Plane parallel to another through a point

Find plane β parallel to α (normal (2, 1, 2), constant -54) through P(16, 11, 7).

Step-by-step solution

1. Two planes are parallel if they have the same normal (or proportional normals).
2. Keep the normal of α and work out the new constant term with point P.
3. Check that P lies on β and does not lie on α.

Result: β: 2x + 1y + 2z − 57 = 0.

If the point lay on α, the plane would coincide with α; it would not be a different plane.

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