For three vectors `vecP, vecQ and vecR, vecP+vecQ=vecR and P+Q=R`
Then prove that `vecP and vecQ` are parallel to each other.

Explanation

To prove that the vectors \(\vec{P}\) and \(\vec{Q}\) are parallel to each other given that \(\vec{P} + \vec{Q} = \vec{R}\) and \(P + Q = R\), we can follow these steps:

### Step 1: Understand the given equations
We are given two equations:
1. \(\vec{P} + \vec{Q} = \vec{R}\) (vector equation)
2. \(P + Q = R\) (magnitude equation)

### Step 2: Use the formula for the magnitude of the resultant of two vectors
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