Shadow Area

Geometry Level pending

A bus stop sign plate (shown in orange) is rectangular and measures \( 5 \times 10 \) units. The normal vector to its plane is along the x-axis. The sun rays shine uniformly (i.e. with uniform direction) on the bus stop, with a direction vector \( \mathbf{u} = \mathbf{i} - 2 \mathbf{j} - 0.5 \mathbf{k} \)

Find the area of the shadow of the rectangular plate on the XY plane.

The elevation of the sign above the XY plane does not change the answer, and can be set to any non-negative value.

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