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Why is the "product of vectors" the multiplication of modules of two vectors and then the multiplication of cos? Is this artificial? Or is there any basis?
This problem is introduced in terms of force and work
Work = force * distance in the direction of force
The problem is: force and direction are vectors. If there is an angle between force and distance, then the product is not work
Therefore, we should first project the force in the direction of distance by multiplying the cosine of the included angle. In this way, we can decompose the force in the distance, and then multiply the distance is the correct work
It extends to all vectors, and that's it
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