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Question: The value of \((\overset{\rightarrow}{A} + \overset{\rightarrow}{B}) \times (\overset{\rightarrow}{A...

The value of (A→+B→)×(A→−B→)(\overset{\rightarrow}{A} + \overset{\rightarrow}{B}) \times (\overset{\rightarrow}{A} - \overset{\rightarrow}{B}) is

A

0

B

A2−B2A^{2} - B^{2}

C

B→×A→\overset{\rightarrow}{B} \times \overset{\rightarrow}{A}

D

2(B→×A→)2(\overset{\rightarrow}{B} \times \overset{\rightarrow}{A})

Answer

2(B→×A→)2(\overset{\rightarrow}{B} \times \overset{\rightarrow}{A})

Explanation

Solution

(A→+B→)×(A→−B→)(\overrightarrow{A} + \overrightarrow{B}) \times (\overrightarrow{A} - \overrightarrow{B}) =A→×A→−A→×B→+B→×A→−B→×B→= \overrightarrow{A} \times \overrightarrow{A} - \overrightarrow{A} \times \overrightarrow{B} + \overrightarrow{B} \times \overrightarrow{A} - \overrightarrow{B} \times \overrightarrow{B}

=0−A→×B→+B→×A→−0=B→×A→+B→×A→=2(B→×A→)= 0 - \overrightarrow{A} \times \overrightarrow{B} + \overrightarrow{B} \times \overrightarrow{A} - 0 = \overrightarrow{B} \times \overrightarrow{A} + \overrightarrow{B} \times \overrightarrow{A} = 2(\overrightarrow{B} \times \overrightarrow{A})