Question

Find the vector equation of each one of following planes. 

x + y − z = 5

 

Answer 1

 `\text{ The given equation of plane is } `

\[x + y - z = 8\]

\[ \Rightarrow \left( \text{ x }\hat{i} + \text{  y} \hat{j}  + \text{ z} \hat{k}  \right) . \left( \hat{i}  + \hat{j}  - \hat{k} \right) = 8\]

\[ \Rightarrow \vec{r} . \left( \hat{i} + \hat{j} - \hat{k} \right) = 8, \text{ which is the vector equation of the plane }.\]

\[(\text{ Because the vector equation of the plane is }  \vec{r} . \vec{n} = \vec{a} . \vec{n} )\]