Consider the vector in .
(a) Find the positive real number such that is a unit vector.
Give your answer exactly (e.g. sqrt(123)), not as a decimal.


(b) Find a vector such that is an orthonormal set in .

What is the norm ("length") of v? (Use Pythagoras to find it.) Divide v by its norm to get a unit vector.
u has to be a unit vector orthogonal to v. The vector (9,6) is obviously orthogonal to v, so take a suitable scalar multiple of it, as in part (a).