If $\overrightarrow a=\hat i+\hat j+\hat k,\:\:\overrightarrow c=\hat j-\hat k$ and $\overrightarrow b$ is such that $\overrightarrow a\times\overrightarrow b=\overrightarrow c\:\:and\:\:\overrightarrow a.\overrightarrow b=3$ then $\overrightarrow b=?$

Question

$\large(a)\:3\hat i-\hat j-\hat k\:\:\qquad\:(b)\:\:\large\frac{1}{3}(5\hat i+2\hat j+2\hat k)\:\:\qquad\:\:(c)\:\:\large\frac{1}{3}(5\hat i-2\hat j-2\hat k)\:\:\qquad\:\:(d)\:\:none\:of\:these.$