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

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

Answers (1)

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

\vec{r}=x\hat{i}+y\hat{j}-z\hat{k}

Putting

\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.

Posted by

infoexpert24

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