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Numerade Educator



Problem 64 Hard Difficulty

Show that if $ u + v $ and $ u - v $ are orthogonal, then the vectors $ u $ and $ v $ must have the same length.


So $|\mathbf{u}|=|\mathbf{v}|$


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Video Transcript

So if you and you posie and humans you're orthogonal That means you plus v don't you mind? His V is going to be equal to zero. So let's see what happens here. So we got you got you minus you. Don't be plus v dot You migh ve dot b is equal is here. So this is really just the magnitude ofyou squared, minus you dot ve plus we can switch these orders. It doesn't really matter. Minus nineteen of the squared. These guys will cancel out get you nine to you squared is equal magnitude of e squared. That means banks interview past vehicle to the magnitude of the so they have the same, like