Given that p = (5, 9) and q = (13, 12), find the component form and magnitude of vector pq.

To calculate for the magnitude of vector PQ, what needs to be done is to determine the distance between them through the two-point equation which is shown below.
  
                               d = sqrt ((x₂ - x₁)² + (y₂ - y₁)²)

Substituting the known values,
                              d = sqrt ((13 - 5)² + (12 - 9)²)
The value of d from the equation is sqrt of 73 or 8.54. 

Therefore, the magnitude of the vector is equal to 8.54.