Q:

The reason behind this answer in the textbook?

Given the following:

Calculate the orthogonal vector: 
The answer in the text book is: 
However when I calculate it I get the following:
$$\frac{1}{\sqrt{-2^{2}+0^{2}+2^{2}}}\begin{bmatrix}
-2\\ 
0\\ 
2
\end{bmatrix}=\frac{1}{\sqrt{8}}\begin{bmatrix}
-2\\ 
0\\ 
2
\end{bmatrix}$$
I realize it is the same answer, however why did the textbook divide by 2 to result in the vector $\begin{bmatrix}
-1\\ 
0\\ 
1
\end{bmatrix}$

A:

You computed $e/\|e\|$, but you missed the obvious fact that $\sqrt{8}=2\sqrt{2}$, and therefore your result coincides with that provided by the book. 
Unless you mean a different thing, the textbook just simplifies the square root of $8$, nothing more, nothing less.

