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Question
Find the vector equation of each one of following planes.
x + y − z = 5
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Solution
`\text{ The given equation of plane is } `
\[x + y - z = 8\]
\[ \Rightarrow \left( \text{ x }\hat{i} + \text{ y} \hat{j} + \text{ z} \hat{k} \right) . \left( \hat{i} + \hat{j} - \hat{k} \right) = 8\]
\[ \Rightarrow \vec{r} . \left( \hat{i} + \hat{j} - \hat{k} \right) = 8, \text{ which is the vector equation of the plane }.\]
\[(\text{ Because the vector equation of the plane is } \vec{r} . \vec{n} = \vec{a} . \vec{n} )\]
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