A) \[7|\overset{\to }{\mathop{a}}\,\times \overset{\to }{\mathop{b}}\,{{|}^{2}}\]
B) \[42|\overset{\to }{\mathop{a}}\,\times \overset{\to }{\mathop{b}}\,{{|}^{2}}\]
C) 0
D) None of these
Correct Answer: B
Solution :
[b] \[\overrightarrow{BD}=\overrightarrow{a}-3\overrightarrow{b},\overrightarrow{AC}=\overrightarrow{a}+3\overrightarrow{b}\] \[\overrightarrow{BD}\times \overrightarrow{AC}=(\overrightarrow{a}-3\overrightarrow{b})\times (\overrightarrow{a}+3\overrightarrow{b})=6\overrightarrow{a}\times \overrightarrow{b}\] \[\overrightarrow{OD}\times \overrightarrow{OC}=(\overrightarrow{a}-2\overrightarrow{b})\times (2\overrightarrow{a}+3\overrightarrow{b})=7\overrightarrow{a}\times \overrightarrow{b}\] \[(\overrightarrow{BD}\times \overrightarrow{AC}).(\overrightarrow{OD}\times \overrightarrow{OC})=42{{(\overrightarrow{a}\times \overrightarrow{b})}^{2}}\]You need to login to perform this action.
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