If $\overrightarrow{a}$a is a unit vector, $\overrightarrow{a}\times \overrightarrow{r}=\overrightarrow{b}, \overrightarrow{a} .\overrightarrow{r}=c$, then $\overrightarrow{r}$ = 

$$\begin{gathered} \overline{\mathrm{a}}\times \overline{\mathrm{r}}=\overline{\mathrm{b}}\Rightarrow \overline{\mathrm{a}}\times (\overline{\mathrm{a}}\times \overline{\mathrm{r}})=\overline{\mathrm{a}}\times \overline{\mathrm{b}} \\ \Rightarrow (\overline{\mathrm{a}}\cdot \overline{\mathrm{r}})\overline{\mathrm{a}}-(\overline{\mathrm{a}}\cdot \overline{\mathrm{a}})\overline{\mathrm{r}}=\overline{\mathrm{a}}\times \overline{\mathrm{b}} \\ (\overline{\mathrm{a}}\cdot \overline{\mathrm{r}})\overline{\mathrm{a}}-\overline{\mathrm{r}}=\overline{\mathrm{a}}\times \overline{\mathrm{b}} \left(\because \left|\overline{\mathrm{a}}\right|=1\right) \\ \Rightarrow \mathrm{c}\overline{\mathrm{a}}-\overline{\mathrm{r}}=\overline{\mathrm{a}}\times \overline{\mathrm{b}}\left(\because \overline{\mathrm{a}}\cdot \overline{\mathrm{r}}=\mathrm{c}\right) \\ \Rightarrow \overline{\mathrm{r}}=\mathrm{c}\overline{\mathrm{a}} - \overline{\mathrm{a}}\times \overline{\mathrm{b}} \end{gathered}$$