Mathematics - Vector Question with Solution | TestHub

Let$\overrightarrow{\mathit{a}}=\hat{i}+2\hat{\mathit{j}}-\hat{\mathit{k}}, \overrightarrow{\mathit{b}}=\hat{\mathit{i}}-\hat{\mathit{j}}$and$\overrightarrow{c}=\hat{\mathit{i}}-\hat{\mathit{j}}-\hat{\mathit{k}}$be three given vectors. If$\overrightarrow{\mathit{r}}$is a vector such that$\overrightarrow{\mathit{r}}\times \overrightarrow{\mathit{a}}=\overrightarrow{\mathit{c}}\times \overrightarrow{\mathit{a}}$and$\overrightarrow{\mathit{r}}·\overrightarrow{b}=0,$then$\overrightarrow{r}·\overrightarrow{a}$is equal to