Find the Cartesian equation of the following | vedclass

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(A) The given vector equation of the plane is $\vec{r} \cdot(\hat{i}+\hat{j}-\hat{k})=2$ ............$(1)$For any arbitrary point $P(x, y, z)$ on the

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$x+y-z=2$

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(A) The given vector equation of the plane is $\vec{r} \cdot(\hat{i}+\hat{j}-\hat{k})=2$ ............$(1)$For any arbitrary point $P(x, y, z)$ on the plane,the position vector $\vec{r}$ is given by $\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}$.Substituting the value of $\vec{r}$ in equation $(1)$,we get:$(x\hat{i} + y\hat{j} + z\hat{k}) \cdot (\hat{i} + \hat{j} - \hat{k}) = 2$Taking the dot product of the vectors:$x(1) + y(1) + z(-1) = 2$$x + y - z = 2$Thus,the Cartesian equation of the plane is $x + y - z = 2$.

Find the Cartesian equation of the following plane: $\vec{r} \cdot(\hat{i}+\hat{j}-\hat{k})=2$

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