IF ` barP + barQ = barR and P=Q = (R )/(sqrt(2))` then find the angles between the pairs of vectors `( barP , barQ ) , ( barQ,barR) and ( barR, barP)` respectively

Explanation

To solve the problem, we need to find the angles between the pairs of vectors \( \bar{P}, \bar{Q}, \bar{R} \) given that \( \bar{P} + \bar{Q} = \bar{R} \) and \( P = Q = \frac{R}{\sqrt{2}} \).

### Step 1: Understand the given equations
From the problem, we have:
1. \( \bar{P} + \bar{Q} = \bar{R} \)
2. \( P = Q = \frac{R}{\sqrt{2}} \)

### Step 2: Substitute the values of \( P \) and \( Q \)
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