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 Fill in the blanks: The Cartesian equation \vec{r}.\left ( \hat{i}+\hat{j}-\hat{k} \right )=2 of the plane is ______.

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By expanding the dot product given in the question, we can get the Cartesian equation of the plane.

Given: \vec{r}.\left ( \hat{i}+\hat{j}-\hat{k} \right )=2



\Rightarrow \left ( x\hat{i}+y\hat{j}+z\hat{k} \right )\left ( \hat{i}+\hat{j}-\hat{k} \right )=2

\Rightarrow x + y - z = 2

Thus, the required Cartesian equation is x + y - z = 2.

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