A Dot Product Range

Problem

Vectors $\vec a, \vec b, \vec c$ satisfy $|\vec a| = |\vec b| = 2$ , $|\vec c| = 1$ , and

(\vec c - \vec a) \cdot (\vec c - \vec b) = 0.

Find the range of $\vec a \cdot \vec b$ .

Answer

Solution

Difficulty	6/10
Topics	Extrema, Substitution, vectors

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