# arrow_back How do I determine the equation of a normal in $R^2$ or $R^3$?

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How do I determine the equation of a normal in $R^2$ or $R^3$?

(a) If $a$ and $b$ are constants that are not both zero, then an equation of the form $$a x+b y+c=0$$ represents a line in $R^{2}$ with normal $\mathbf{n}=(a, b) .$

(b) If $a, b$, and $c$ are constants that are not all zero, then an equation of the form $$a x+b y+c z+d=0$$ represents a plane in $R^{3}$ with normal $\mathbf{n}=(a, b, c)$.
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