How is the length of a vector in R^{3} defined?
Let u = (u1, u2, u3) be a vector in R
3
. Prove that ||u|| = 0 if and only if u = 0.
[Note: the ‘if and only if’ phrase means that you have to prove TWO things - ﬁrstly, that
||u|| = 0 implies u = 0; and secondly, that u = 0 implies ||u|| = 0.]