First slide

Vectors

Question

The value of $(\vec{A} + \vec{B}) \times (\vec{A} - \vec{B})$ is

Moderate

A

0
B

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

$\vec{B} \times \vec{A}$
D

$2 (\vec{B} \times \vec{A})$

Solution

$(\vec{A} + \vec{B}) \times (\vec{A} - \vec{B}) = \vec{A} \times \vec{A} - \vec{A} \times \vec{B} + \vec{B} \times \vec{A} - \vec{B} \times \vec{B}$
$= 0 - \vec{A} \times \vec{B} + \vec{B} \times \vec{A} - 0$
= $\vec{B} \times \vec{A} + \vec{B} \times \vec{A} = 2 (\vec{B} \times \vec{A})$

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