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The line of steepest slope of a plane is the one that makes the largest possible angle with the horizontal plane. It is perpendicular to the horizontal trace of the plane and lies in it. The line of steepest inclination is perpendicular to the vertical trace.
Plane α meets the PH along its trace α₁. All lines of steepest slope are perpendicular to that trace.
In exams it is useful for everything: it is the line rotated flat to measure the slope of the plane and the one used to draw planes with a given inclination.