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3-1.Vectors
medium
The value of $(\overrightarrow A + \overrightarrow B )\, \times (\overrightarrow A - \overrightarrow B )$ is
A
$0$
B
${A^2} - {B^2}$
C
$\overrightarrow B \times \overrightarrow A $
D
$2(\overrightarrow B \times \overrightarrow A )$
Solution
(d)$(\vec A + \vec B) \times (\vec A – \vec B)$
$ = \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)$
Standard 11
Physics
