So the question is:
Which of the following sets of vectors form an orthonormal basis for $\mathbb{R}^2$
$(a) \{(1,0)^T, (0,1)^T\}$
$(b) \{(\frac{3}{4},\frac{4}{5})^T,(\frac{5}{13},\frac{12}{13})^T\}$
I know that a is a basis and b is not. The thing is, I just don't know why. I know the definition of orthonormal is if two vectors are perpendicular and of unit length. But I don't understand how to prove or even find for that matter, the orthonormal basis of a space. Any ideas? Thanks