A) \[\sqrt{\frac{11}{3}}\]
B) \[\sqrt{\frac{11}{3}}\]
C) \[\frac{11}{\sqrt{3}}\]
D) \[\frac{11}{3}\]
Correct Answer: A
Solution :
\[\vec{a}\times \vec{b}\times \vec{c}\] \[\Rightarrow \]\[|\vec{a}||\vec{b}|\sin \theta =|\vec{c}|\] \[\Rightarrow \]\[|\vec{a}||\vec{b}|\sin \theta =\sqrt{2}\] ?[1] \[\vec{a}.\vec{b}=3\] \[\Rightarrow \]\[|\vec{a}||\vec{b}|\cos \theta =3\] ?[2] Dividing [1] by [2], we get \[\tan \theta =\frac{\sqrt{2}}{3}\] \[\Rightarrow \]\[\sin \theta =\frac{\sqrt{2}}{\sqrt{11}}\] Substituting value of \[\sin \theta \]in [1], we get \[\Rightarrow \]\[|\vec{a}||\vec{b}||\sin \theta |=\sqrt{2}\] \[\Rightarrow \]\[\sqrt{3}|\vec{b}|\frac{\sqrt{2}}{\sqrt{11}}=\sqrt{2}\] \[|\vec{b}|=\frac{\sqrt{11}}{\sqrt{3}}\] Hence, answer is option A.
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