Why is $\vec a\downarrow\vec c=\vec a\downarrow(\vec b\downarrow\vec c)$? I know how to draw a driagram to show that it's true, but I can't really explain it mathematically / algebraically. This is about projection vectors, if the notation is unclear.
EDIT:
This is the notation I've learned, but after having read about more standard notation, I see that more people would prefer it this way:
$$Proj_\vec c\vec a=Proj_{proj_\vec c\vec b}\vec a$$

The projection can be written as $$\vec a \downarrow \vec c=\frac{\vec c\cdot \vec a}{\vec c \cdot \vec c}\vec c$$
What do you get if you let $\vec c=\vec b \downarrow \vec c$?
