MCQ
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 $
- ✓$2(\overrightarrow B \times \overrightarrow A )$
✓
Answer
Correct option: D.
$2(\overrightarrow B \times \overrightarrow A )$
d
(d)$(\vec A + \vec B) \times (\vec A - \vec B)$
(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)$
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