A Diagonal Dot Identity

★ 6/10plane geometry Polarization Identity vectors

Problem

In quadrilateral $ABCD$ , the diagonals satisfy $AC = a$ and $BD = b$ . Find

\left(\overrightarrow{AB} + \overrightarrow{DC}\right)\cdot\left(\overrightarrow{BC} + \overrightarrow{AD}\right)

in terms of $a$ and $b$ .

Answer

Solution

Difficulty	6/10
Topics	plane geometry, Polarization Identity, vectors

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