A) 0
B) \[-24\]
C) 3600
D) \[-215\]
E) 360
Correct Answer: D
Solution :
\[[\overrightarrow{a}-2\overrightarrow{b},\overrightarrow{b}-3\overrightarrow{c},\overrightarrow{c}-4\overrightarrow{a}]\] \[=(\overrightarrow{a}-2\overrightarrow{b}).\{(\overrightarrow{b}-3\overrightarrow{c})\times (\overrightarrow{c}-4\overrightarrow{a})\}\] \[=(\overrightarrow{a}-2\overrightarrow{b}).\{\overrightarrow{b}\times \overrightarrow{c}-4\overrightarrow{b}\times \overrightarrow{a}+12\overrightarrow{c}\times \overrightarrow{a}\}\] \[=(\overrightarrow{a}-2\overrightarrow{b}).(\overrightarrow{a}+4\overrightarrow{c}+12\overrightarrow{b})\] \[=\overrightarrow{a}.\overrightarrow{a}-24\overrightarrow{b}.\overrightarrow{b}\] \[=1-24\times 9\] \[=1-216=-215\]You need to login to perform this action.
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