Three Dimensional Geometry — Class 12 Maths Solution

It is given that, $\overrightarrow {\rm{r}} \cdot (\widehat {\rm{i}} + \widehat {\rm{j}} - \widehat {\rm{k}}) = 2$

$\Rightarrow$ $(x\widehat {\rm{i}} + y\widehat {\rm{j}} + z\widehat {\rm{k}}) \cdot (\widehat {\rm{i}} + \widehat {\rm{j}} - \widehat {\rm{k}}) = 2$

$\Rightarrow$ $x + y - z = 2$

which is the required form