Well the length of a vector [a,b,c,...] is

so the legnth of u would be

which is what you got, you just need to provide it as a squareroot for the "exact answer"

Sorry i can't help with (b), but for (c) a vector in the opposite direction has the negative of the components of the original vector. e.g. the opposite direction to [a,b,c,d] is [-a,-b,-c,-d], so the opposite direction to w=[0,2,-2,2] is [0,-2,2,-2]. A

**unit** vector in this direction has a length of 1, so it is some positive multiple k of [0,-2,2,-2] which has a length of 1. Calculate the length using the above formula.

so the unit vector in the direction opposite to w=[0,2,-2,2] is

Hope this helps