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