Question
Show that $\left( {\vec a - \vec b} \right) \times \left( {\vec a + \vec b} \right) = 2\left( {\vec a \times \vec b} \right)$
$= \vec a \times \vec a + \vec a \times \vec b - \vec b \times \vec a - \vec b \times \vec b$
$= 0 + \vec a \times \vec b + \vec a \times \vec b - 0$ $[as \ \vec a×\vec b=-\vec b×\ \vec a]$
$=2(\vec a×\vec b)$
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