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Line perpendicular to a plane

Statement. Through point P(2, 4, 6), draw the line perpendicular to plane P: y = 4.

Step-by-step solution

1. Plane P is parallel to the vertical plane, so it is seen edge-on in the plan: its trace is the line y = 4.
2. A line perpendicular to a plane is perpendicular to all its lines, and its direction is the normal of the plane.
3. The normal of y = 4 is (0, 1, 0): a line pointing straight at the viewer, perpendicular to the trace in the plan.
4. Draw it through P: in the elevation it looks like a point (P'') and in the plan as a perpendicular to the trace.

Result

Line through P(2, 4, 6) with direction (0, 1, 0).

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