(Pythagoras's Theorem) Prove by vector method that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Explanation

To prove the Pythagorean theorem using vector methods, we can follow these steps:

### Step 1: Define the Right Triangle
Let triangle ABC be a right-angled triangle with the right angle at point A. We can denote the lengths of the sides as follows:
- AB = c (hypotenuse)
- AC = a
- BC = b

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