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