A Tetrahedron Dot Range

Problem

A regular tetrahedron $ABCD$ has edge length $2\sqrt{2}$ , and a point $P$ satisfies

\left|\overrightarrow{PA} + \overrightarrow{PB}\right| = 2.

Find the minimum and maximum values of $\overrightarrow{AP}\cdot\overrightarrow{AD}$ .

Answer

Solution

Difficulty	7/10
Topics	Extrema, solid geometry, vectors

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