\(\overline{\mathrm{a}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}, \overline{\mathrm{~b}}=\hat{\mathrm{j}}-\hat{\mathrm{k}}\), then vector \(\overline{r}\) satisfying \(\overline{\mathrm{a}} \times \overline{\mathrm{r}}=\overline{\mathrm{b}}\) and \(\overline{\mathrm{a}} \cdot \overline{\mathrm{r}}=3\) is
1
\(\frac{5}{3} \hat{\mathrm{i}}+\frac{2}{3} \hat{\mathrm{j}}+\frac{2}{3} \hat{\mathrm{k}}\)
2
\(-\frac{5}{3} \hat{\mathrm{i}}+\frac{2}{3} \hat{\mathrm{j}}+\frac{2}{3} \hat{\mathrm{k}}\)
3
\(\frac{5}{3} \hat{\mathrm{i}}-\frac{2}{3} \hat{\mathrm{j}}+\frac{2}{3} \hat{\mathrm{k}}\)
4
\(-\frac{5}{3} \hat{\mathrm{i}}+\frac{2}{3} \hat{\mathrm{j}}+\frac{1}{3} \hat{\mathrm{k}}\)