Remember that the unit-vector form is a vector equation that relates a vector to its x, y, and z components:
Anytime we're asked to relate the magnitude and direction of a three-dimensional vector to its components, there are four basic equations we might use:
(a) For this problem we're given that . Plugging these magnitudes into equation (1), we get
The magnitude of the vector is 33.3 units.
(b) For the second part of the problem, we solve equations 2-4 for the angle and substitute our known values: