Question

Find the Cartesian form of the equation of a plane whose vector equation is 

  \[\vec{r} \cdot \left( - \hat{i} + \hat{j}  + 2 \hat{k} \right) = 9\]

 

Answer 1

`  \text{ Substituting }  \vec{r} =\text{ x }\hat{i}  +\text{  y }\hat{j}  +\text{  z }\hat{k}  \text{ in the given equation, we get } `
\[\left(  \text{ x }\hat{i}  +\text{ y }\hat{j}  + \text{  z }\hat{k}  \right) . \left( - \hat{i}  + \hat{j}  + \text{ 2 }\hat{k}  \right) = 9\]
\[ \Rightarrow - x + y + 2z = 9\]