(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

Please refer to video to see the triangle `ABC`.

Here, `vec (AC) = vec(AB) + vec(BC)`

`=>vec (AC)*vec (AC) = ( vec(AB) + vec(BC))*( vec(AB) + vec(BC))`

`=>|vec(AC)|^2 = |vec(AB)|^2+2vec(AB)*vec(BC)+|vec(BC)|^2`

Now, `vec(AB)*vec(BC) = 0`

`:.|vec(AC)|^2 =|vec(AB)|^2+|vec(BC)|^2`, which is pyhagoras theorem.