A) 343
B) 512
C) 221
D) 243
Correct Answer: A
Solution :
\[\vec{V}=\vec{A}\times \left[ (\vec{A}.\vec{B})\vec{A}-(\vec{A}.\vec{A})\vec{B} \right].\vec{C}\] \[=\left( \underbrace{\vec{A}\times (\vec{A}.\vec{B})\vec{A}}_{zero}-(\vec{A}.\vec{A})\vec{A}\times \vec{B} \right).\vec{C}=-|\vec{A}{{|}^{2}}[\vec{A}\vec{B}\vec{C}]\]Now, \[|\vec{A}{{|}^{2}}=4+9+36=49\] \[[\vec{A}\vec{B}\vec{C}]=\left| \begin{matrix} 2 & 3 & 6 \\ 1 & 1 & -2 \\ 1 & 2 & 1 \\ \end{matrix} \right|\] \[=2(1+4)-2(3-12)+1(-6-6)\] \[=10+9-12=7\] \[\therefore \]\[\left| -|\vec{A}{{|}^{2}}[\vec{A}\vec{B}\vec{C}] \right|=49\times 7=343\]You need to login to perform this action.
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