[Tex/LaTex] Wrong scaling in xyz coordinate systems

tikz-pgf

As stated in the Manual in section 10.2.1 "the default z-vector points to (-sqrt(2), -sqrt(2)).
But when I draw:

\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[axis/.style={thick,->}]
    \coordinate (O) at (0, 0, 0);
    \draw[axis] (O) -- +(1, 0, 0) node [right] {$X$};
    \draw[axis] (O) -- +(0, 1, 0) node [right] {$Y$};
    \draw[axis] (O) -- +(0, 0, 1) node [above] {$Z$};
    \draw[red, thick]   (O) -- +(-0.70710678, -0.70710678);
\end{tikzpicture}
\end{document}

I get this:

TikZ output

As you can see: the red line is clearily longer than the z-axis, whereas it should be equal in length.
Can someone point me to the right direction?

During my investigations I found another strange behaviour:

\documentclass[11pt]{minimal}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
    \draw[red]          (-2cm,-2cm) grid (3,2cm);
    \coordinate         (O) at (0, 0, 0);
    \draw[blue]         (O) -- +(0, 1cm, 0);
\end{tikzpicture}
\end{document}

Yields two pages: the first one is empty, and the second one looks like:

output

This is the whole page, I didn't clip anything.

I am totally confused.

Best Answer

All credit goes to Jake!

This answer is based on his comments:

The first problem was based on an old version of the manual which I used. In the current manual they state, that the default z vector points to (−3.85mm, −3.85mm), which is correct.

For the solution of my second problem, I'm citing Jake:

The second behaviour happens because the 1cm in (0,1cm,0) is interpreted not as a length, but as a multiplier of the unit vector after converting 1cm to 28.45pt, so your blue line is 28.45cm long. This looks like a bug, or at least unexpected behaviour

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