# Quod Erat Demonstrandum

## 2008/01/04

### cosine of a vector

Filed under: Uncategorized — johnmayhk @ 6:10 下午

After school, a F.5 student, Yan, discussed some mathematics matters with me, what a wonderful moment! One of the questions he asked was

“is it possible to define the cosine value of a vector?"

I just claimed that it is easy for finite dimensional or even countably infinite dimensional vector, for example, we may have something like

$V:= v_1e_1 + v_2e_2 + \dots$, then
$\cos(V):= \cos(v_1)e_1 + \cos(v_2)e_2 + \dots$

And actually, we may define $f(V) = W$ where $V, W$ are vectors (even in different dimensional spaces). And it is just a beginning…

I don’t think I had asked my teachers something like that when I was a F.5 boy. Sharing and exploring mathematics is fun!