Geometric proof of dot product distributive property I'm working my way through a text book for fun in order to keep my math brain fresh and came across this simple yet perplexing problem.
"Demonstrate geometrically that the dot product is distributive"
I can do this algebraically but what would a geometric proof of this look like?

Maybe something like this?
$$a \cdot (b+c) = a \cdot b + a \cdot c$$
"The 'projection' of $a$ onto $b+c$ is the same as the sums of the 'projections' of $a$ onto $b$ and of $a$ onto $c$." (You'll have to draw the triangle formed by $b$, $c$, and $b+c$. Also, you will need to be precise about what the 'projection' is.)
