Show that for two vectors v and w of a Euclidean vector space V we have |v+w| ≤ |v|+ |w|.
Can anybody help with this please?
First you will need the cauchy-schwarz inequality $\displaystyle <v,w> \le |v||w|$
Now starting with the square we get
$\displaystyle |v+w|^2=<v+w,v+w>=<v,v>+<w,w>+2<v,w> \le $
$\displaystyle |v|^2+|w|^2+2|v||w|=(|v|+|w|)^2$
Now we take the square root and we are done.