( A^ → + B^ → ) × ( A^ → - B^ → ) का मान

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$(\mathop A\limits^ \to + \mathop B\limits^ \to )\, \times (\mathop A\limits^ \to - \mathop B\limits^ \to )$ का मान है

A

$0$

B

${A^2} - {B^2}$

C

$\mathop B\limits^ \to \times \mathop A\limits^ \to $

D

$2(\mathop B\limits^ \to \times \mathop A\limits^ \to )$

$(\mathop A\limits^ \to + \mathop B\limits^ \to )\, \times (\mathop A\limits^ \to - \mathop B\limits^ \to )$ का मान है

$(\vec A + \vec B) \times (\vec A - \vec B)$

$ = \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 B \times \vec A - 0$

$ = \vec B \times \vec A + \vec B \times \vec A = 2(\vec B \times \vec A)$