A

Step 1: Recall that the resultant vector of two perpendicular vectors P and Q can be expressed using the Pythagorean theorem.
Step 2: When two vectors are perpendicular, their resultant vector is calculated as follows:
$$ R = \sqrt{P^2 + Q^2} $$
Step 3: If the resultant is perpendicular to one of the vectors (let's say P), the angle between the two vectors P and Q must be 90 degrees.
Thus, the angle between P and Q is \(90^\circ\).
Therefore, the answer is A.