A) \[5\sqrt{3}\]
B) 6
C) \[4\sqrt{3}\]
D) 9
E) \[6\sqrt{3}\]
Correct Answer: E
Solution :
\[|\overrightarrow{x}\times \overrightarrow{y}|=|(\overrightarrow{a}+\overrightarrow{b})\times (\overrightarrow{a}-\overrightarrow{b})|\] \[=|-\overrightarrow{a}\times \overrightarrow{b}+\overrightarrow{b}\times \overrightarrow{a}|\] \[=2|\overrightarrow{a}\times \overrightarrow{b}|\] \[=2|\overrightarrow{a}||\overrightarrow{b}|\sin \frac{\pi }{3}\] \[=2\times 2\times 3\times \frac{\sqrt{3}}{2}\] \[=6\sqrt{3}\]
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