Show that (a-b) (a+b)=2(a b) - Vidyadip

Question

Show that $(\vec{a}-\vec{b}) \times(\vec{a}+\vec{b})=2(\vec{a} \times \vec{b})$

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Answer

Using distributive property $(a-b) \times(a+b)=a \times a+a \times b-b \times a-b \times b(\because a \times b=-b \times a)$
$
\begin{aligned}
& =\overline{0}+\bar{a} \times \bar{b}+\bar{a} \times \bar{b}-\overline{0}(\because \bar{a} \times \bar{a}=\overline{0}) \\
& =2(\bar{a} \times \bar{b})
\end{aligned}
$

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