Direction cosine without dot product

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What is direction cosine?How to compute them and associate with unit vector.This presentation do not use dot product, as it is introduced in Howard Anton's Calculus text..
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Thank you.  Very well presented and easy to understand.

erikajames
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Thanks man, you really made me understand it better!

mavadim
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thank you so much. this helped me a lot :)

prabakaran