Question

The cartesian equation of the plane $\overrightarrow{r}·(\hat{i}+\hat{j}+\hat{k})=2$ is _____________.

Answer 1

The cartesian equation of the plane

$$\begin{gathered} \overrightarrow{r}.\left(\hat{i}+\hat{j}+\hat{k}\right)=2 \\ \mathrm{for}\overrightarrow{r}=\left(x\hat{i}+y\hat{j}+z\hat{k}\right) \\ \mathrm{is}\left(x\hat{i}+y\hat{j}+z\hat{k}\right).\left(\hat{i}+\hat{j}+\hat{k}\right)=2 \\ \mathrm{i}.\mathrm{e}.x+y+z=2\mathrm{is}\mathrm{the}\mathrm{cartesian}\mathrm{equation} \end{gathered}$$