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Question
Find the Cartesian form of the equation of a plane whose vector equation is
\[\vec{r} \cdot \left( - \hat{i} + \hat{j} + 2 \hat{k} \right) = 9\]
Solution
` \text{ Substituting } \vec{r} =\text{ x }\hat{i} +\text{ y }\hat{j} +\text{ z }\hat{k} \text{ in the given equation, we get } `
\[\left( \text{ x }\hat{i} +\text{ y }\hat{j} + \text{ z }\hat{k} \right) . \left( - \hat{i} + \hat{j} + \text{ 2 }\hat{k} \right) = 9\]
\[ \Rightarrow - x + y + 2z = 9\]
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