Question

Find the vector equation of each one of following planes. 

x + y = 3

 

Answer 1

`  \text{ The given equation of plane is } ` 
\[x + y = 3\]
\[ \Rightarrow \left( \text{  x} \hat{i}  +  \text{  y }\hat{j}  +  \text{ z} \hat{k}  \right) . \left( \hat{i}  + \hat{j} + 0 \hat{k} \right) = 3\]
\[ \Rightarrow \left( \text{ x }  \hat{i} + \text{ y }\hat{j} + \text{ z } \hat{k}  \right) . \left( \hat{i}  + \hat{j}  \right) = 3\]
\[ \Rightarrow \vec{r} . \left( \hat{i}  + \hat{j}  \right) = 3, \text{ which is the vector equation of the plane } .\]
\[(\text{ Because the vector equation of the plane is }  \vec{r} . \vec{n} = \vec{a} . \vec{n} )\]