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**Finroe** First off, thanks for the prompt replies. Ive used the hints and theyve been very helpful. i overlooked the fact that two perpindicular vectors have a dot product of 0, our dot product unit was a while ago. I was just wondering, if anyone has tried solving this problem and if they have, how long is their solution. My proof is close to 3/4 of a page and i still havent proved the equality. let me know if you managed to solve this and how logn the proof was. thanks again.