Question

The following defines an inner product on R2:
<(x,y),(a,b)>= 3xa-xb-ya+yb

u=(1,0) v=(0,1) and w=(1,3)

a) Find a vector of length 1 with respect to this inner product that is parallel to u.
b) Calculate the angle between u and v with respect to this inner product.
c)Show that the set {u,w} is orthogonal. Is the set orthonormal ? (Justify your answer.)