question_answer

If \[\overrightarrow{a}=\hat{i}+\hat{j}+\hat{k},\] \[\overrightarrow{c}=\hat{j}-\hat{k}\] are given vectors, then find a vector \[\overrightarrow{b}\] satisfying the equations \[\overrightarrow{a}\times \overrightarrow{b}=\overrightarrow{c}\]and \[\overrightarrow{a}\times \overrightarrow{b}=3\].

A)  \[\frac{3}{5}\hat{i}+\frac{4}{5}\hat{j}+\frac{2}{5}\hat{k}\]    

B)  \[\frac{5}{3}\hat{i}+\frac{2}{3}\hat{j}+\frac{2}{3}\hat{k}\]

C)  \[\frac{1}{5}\hat{i}+\frac{2}{5}\hat{j}+\frac{3}{5}\hat{k}\]    

D)  \[\frac{2}{3}\hat{i}+\frac{5}{3}\hat{j}+\frac{4}{3}\hat{k}\]

E)  None of these