The sum and difference of two vectors are perpendicular to each other. Prove that the vectors are equal in magnitude.

Explanation

To prove that two vectors \( \vec{A} \) and \( \vec{B} \) are equal in magnitude given that their sum and difference are perpendicular, we can follow these steps:

### Step 1: Define the vectors
Let the two vectors be \( \vec{A} \) and \( \vec{B} \).

### Step 2: Write the expressions for the sum and difference
The sum of the vectors is given by:
\[
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