A) 3
B) \[-5\]
C) \[-3\]
D) 5
Correct Answer: B
Solution :
We have \[\left( 2\vec{a}-\vec{b} \right).\left[ \left( \vec{a}\times \vec{b} \right)\times \left( \vec{a}+2\vec{b} \right) \right]\] \[=\left( 2\vec{a}-\vec{b} \right).\left( \vec{b}-2\vec{a} \right)\] \[=-{{\left( 2\vec{a}-\vec{b} \right)}^{2}}\] \[=-\left[ 4{{\left| {\vec{a}} \right|}^{2}}+{{\left| {\vec{b}} \right|}^{2}}-4\vec{a}.b \right]\] \[=-\left[ 4+1 \right]=-5\]
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