Find unit vector perpendicular to x-z,x-y, and y-z plane

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I'm guessing that the unit vector perpendicular to the x-z plane is $\begin{bmatrix}1\\0\\1\end{bmatrix}$

I'm guessing that the unit vector perpendicular to the x-y plane is $\begin{bmatrix}1\\1\\0\end{bmatrix}$

I'm guessing that the unit vector perpendicular to the y-z plane is $\begin{bmatrix}0\\1\\1\end{bmatrix}$

Am I correct?

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1 Answer

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Firstly, none of your suggestions are unit vectors since in all cases $|{\mathbf{v}}| = \sqrt{2}$.

You can check that

• a normal to $xz$-plane: $(0,1,0)$
• a normal to $xy$-plane: $(0,0,1)$
• a normal to $yz$-plane: $(1,0,0)$

by taking the dot with the relevant unit vectors in the $x,y,z$ directions.

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