# Math Help - Euclidean vector space

1. ## Euclidean vector space

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?

2. Originally Posted by jackiemoon
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 $ \le |v||w|$

Now starting with the square we get

$|v+w|^2==++2 \le$
$|v|^2+|w|^2+2|v||w|=(|v|+|w|)^2$

Now we take the square root and we are done.