The resultant vector of `vec(P)` and `vec(Q)` is `vec(R )`. On reversing the direction of `vec(Q)` the resultant vector becomes `vec(S)`. Show that `R^(2)+S^(2)=2(P^(2)+Q^(2))`

Explanation

To solve the problem, we need to show that \( R^2 + S^2 = 2(P^2 + Q^2) \) given the vectors \( \vec{P} \), \( \vec{Q} \), \( \vec{R} \), and \( \vec{S} \).

### Step 1: Define the Resultant Vectors
The resultant vector \( \vec{R} \) when vectors \( \vec{P} \) and \( \vec{Q} \) are added is given by:
\[ \vec{R} = \vec{P} + \vec{Q} \]

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