A) \[\frac{2\sqrt{2}}{3}\]
B) \[\frac{\sqrt{2}}{3}\]
C) \[\frac{2}{3}\]
D) \[\frac{1}{3}\]
Correct Answer: A
Solution :
We have , \[(a\times b)\times c=\frac{1}{3}|b|c|a\] \[\Rightarrow \] \[(a.c)b-(b.c).a=\frac{1}{3}|b|c|a\] \[\Rightarrow \] \[(a.c)b-\left\{ (b.c)+\frac{1}{3}|b|c| \right\}a=0\] As a and b are not parallel, \[(a.c)=0\]and \[b.c+\frac{1}{3}|b|c|=0\] \[\Rightarrow \] \[|b|c|\cos \theta +\frac{1}{3}|b|c|=0\] \[\Rightarrow \] \[\cos \theta =-\frac{1}{3}\] \[\therefore \] \[\sin \theta =\sqrt{1-{{\cos }^{2}}\theta }=\sqrt{1-\frac{1}{9}}\] \[=\sqrt{\frac{8}{9}}=\frac{2\sqrt{2}}{3}\]You need to login to perform this action.
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