i don't know how to answer this textbook question and to define if it's orthonormal or orthogonal.
the question is: $(P,Q)= \sum_{k=0}^2 P(k)Q(k)$ is defined to be an inner product space in $R_3[x]$, and let $P_1=1$ $P_2=x-1$ $P_3=x^2-2x+\frac{1}{3}$. are ${(P_1,P_2,P_3)}$ orthonormal or orthogonal?
since Q(k) is not given, i don't know how to approach it at all. for it to be orthogonal, the inner product should equal to 0 and each different element in it should be perpendicular to each other, and for it to be orthonormal the length of the unit vector should be 1.
but i don't know how to determine if it's just orthogonal or aso orthonormal. would like your help with it please.