A) 9 cu unit
B) 729 cu unit
C) 81 cu unit
D) 27 cu unit
E) 243 cu unit
Correct Answer: C
Solution :
Let \[\overrightarrow{A}=\overrightarrow{a}\times \overrightarrow{b},\overrightarrow{B}=\overrightarrow{b}\times \overrightarrow{c},\overrightarrow{C}=\overrightarrow{c}\times \overrightarrow{a}\] Given, \[[\overrightarrow{A}\overrightarrow{B}\overrightarrow{C}]=9\,cu\,unit\] Now, \[[\overrightarrow{A}\times \overrightarrow{B}\,\,\,\overrightarrow{B}\times \overrightarrow{C}\,\,\,\overrightarrow{C}\times \overrightarrow{A}]\] \[=(\overrightarrow{A}\times \overrightarrow{B}).[(\,\overrightarrow{B}\times \overrightarrow{C})\times (\,\,\overrightarrow{C}\times \overrightarrow{A})]\] \[=(\overrightarrow{A}\times \overrightarrow{B}).[[(\,\overrightarrow{B}\times \overrightarrow{C}).\overrightarrow{A}]\overrightarrow{C}-[(\overrightarrow{B}\times \overrightarrow{C}).\,\,\overrightarrow{C}]\overrightarrow{A}]\] \[=(\overrightarrow{A}\times \overrightarrow{B}).[[(\,\overrightarrow{B}\overrightarrow{C}\overrightarrow{A}]\overrightarrow{C}-0]\] \[={{[\overrightarrow{A}\overrightarrow{B}\overrightarrow{C}]}^{2}}={{9}^{2}}\] \[=81\text{ }cu\text{ }unit\]You need to login to perform this action.
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