If the vectors `3vecP+vecq, 5vecP - 3vecq and 2 vecp+ vecq, 4 vecp - 2vecq` are pairs of mutually perpendicular vectors, the find the angle between vectors `vecp and vecq`.

Explanation

To solve the problem, we need to find the angle between the vectors \( \vec{p} \) and \( \vec{q} \) given that the vectors \( 3\vec{p} + \vec{q} \), \( 5\vec{p} - 3\vec{q} \) and \( 2\vec{p} + \vec{q} \), \( 4\vec{p} - 2\vec{q} \) are mutually perpendicular pairs.

### Step 1: Set up the equations for mutual perpendicularity
Since the vectors are mutually perpendicular, their dot products must equal zero.

1. For the first pair:
\[
(3\vec{p} + \vec{q}) \cdot (5\vec{p} - 3\vec{q}) = 0
...