Usually people (including, for instance, Calculus teachers) draw the $xyz$ coordinate system in such a way that the $y$ and $z$ axes are perpendicular to each other:
Imagine I actually got three sticks together to make a physical $xyz$ coordinate system. I suspect there is no point of view from which I can look at it and see the picture above. My reasoning is that, if the $y$ and $z$ axes are perpendicular to each other (when drawn), then the $x$ axis must become either
$A$) a point or
$B$) an extension of one of the other axes
but neither $A$ nor $B$ is the case in the first image. So why do people draw the $xyz$ coordinate system like that instead of something like the following?:
Am I missing something?