Suppose we have three independent random variables $X$, $Y$ and $Z$ so the correlation among them is zero. However, I'm struggling to express them using a chart and the fact that correlations are cosines.
If I wanted to draw a chart similar to the one here, I first draw the vectors $X$ and $Y$. The two vectors would form a 90 degree angle. How should I draw $Z$ then? $Z$ can either form a 90 degree angle with $X$ or $Y$, but either way, it would imply a 180 degree or zero degree angle with the other random variable (so the correlation is -1 or 1). How should I visualize this?