A) \[\vec{0}\]
B) \[0\]
C) \[\vec{a}\times \vec{b}\]
D) \[\vec{b}\times \vec{a}\]
Correct Answer: A
Solution :
\[(2\vec{a}+3\vec{b})\times (5\vec{a}+7\vec{b})+\vec{a}\times \vec{b}\] \[=10(\vec{a}\times \vec{a})+14(\vec{a}\times \vec{b})+15(\vec{b}\times \vec{a})\] \[+21(\vec{b}\times \vec{b})+\vec{a}\times \vec{b}\] \[=\vec{0}+14(\vec{a}\times \vec{b})-15(\vec{a}\times \vec{b})+\vec{0}+\vec{a}\times \vec{b}\] \[=\vec{0}\]
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