In particular, take v= u.

Same suggestion- take w= v.c) Show that < v, w > = 0 for any w in V implies that v = 0.

I did part a) like this:

< 0, v > = < 0 + 0, v > = < 0, v > + < 0, v>

< 0, v > = < 0, v > + < 0, v >

< 0, v > - < 0, v > = < 0, v >

0 = < 0, v>

Now I have been trying to prove parts b) and c) but I cannot think of a way to start. The statements both seem so obvious but I don't know where to begin with a proof.