A) 0
B) \[{{A}^{2}}-{{B}^{2}}\]
C) \[\overrightarrow{B}\times \overrightarrow{A}\]
D) \[2(\overrightarrow{B}\times \overrightarrow{A})\]
Correct Answer: D
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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