Show that the normal vector to the plane `2x+2y+2z=3` is equally inclined with the coordinate axes.

Explanation

The vector equation of the plane `2 x+2 y+2 z=3 `can be written as


`(x \hat{\i}+y \hat{\j}+z \hat{k})(2 \hat{\i}+2 \hat{\j}+2 \hat{k})=3 `


`\Rightarrow \vec{r} \cdot(2 \hat{\i}+2 \hat{\j}+2 \hat{k})=3`


The normal to this plane is` \vec{n}=2 \hat{i}+2 \hat{j}+2 \hat{k} \ldots (i)`


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