If `|vec(P) + vec(Q)| = |vec(P) - vec(Q)|` , find the angle between `vec(P)` and `vec(Q)`.

Explanation

To solve the problem, we need to find the angle between the vectors \(\vec{P}\) and \(\vec{Q}\) given that \(|\vec{P} + \vec{Q}| = |\vec{P} - \vec{Q}|\).

### Step 1: Square both sides of the equation
We start with the equation:
\[ |\vec{P} + \vec{Q}| = |\vec{P} - \vec{Q}| \]
Squaring both sides gives us:
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