Locus on a Cube Under a Perpendicularity Condition

Problem

In a cube $ABCD\text{-}A_1B_1C_1D_1$ of edge length $2$ , let $E$ be the midpoint of edge $AA_1$ . A point $P$ moves over the surface of the cube subject to the condition $\overrightarrow{D_1P}\perp\overrightarrow{CE}$ . Let $W$ be the curve traced by $P$ .

Determine the shape of $W$ and find its perimeter.

Answer

Solution

Difficulty	6/10
Topics	solid geometry, Symmetry, vectors

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