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