Final answer:
The angle between vector P and Q is 90 degrees because the dot product equals the product of their magnitudes only when the vectors are perpendicular to each other.
Step-by-step explanation:
If the product of the dot product vector P.Q is equal to the product of the magnitudes of the vectors PQ, this implies that the angle between vector P and Q is 90 degrees. This is because the dot product of two vectors is given by P.Q = |P||Q|cos(θ), where θ is the angle between the two vectors. When P.Q equals PQ, it means that cos(θ) = 1, which occurs when θ is 0 degrees. However, given that the angle is measured from 0° to 180°, the only other possibility for cos(θ) to be 1 is when the angle is 90 degrees, meaning the vectors are orthogonal, or perpendicular, to each other.