For this question, I'm having trouble with this proof. Here is what I have so far. Can anyone please help me out?
Use the triangle inequality to prove that
$||v-w|| \le ||v|| + ||w||$ for any vectors v and w in an inner-product space $V$.
$||v-w||^2$
= $ <v-w,v-w>$
= $ <v,v> - <v,w> - <w,v> + <w,w>$
= $ ||v||^2 -<v,w>-<w,v>+||w||^2$