Remember that two vectors are parallel if their dot product is the product of their magnitudes (in this case, 1), and perpendicular if their dot product is zero. Just by knowing the coordinates and nothing else, you can tell whether the vectors are parallel or perpendicular.
In general, if and are two unit vectors, then
where is the angle between vectors a and b, . In this case, the magnitudes of a and b are 1, so .