- #36
FireStorm000
- 169
- 0
nouveau, you quote me in support of your argument that work is a vector, but if you continue reading I later realized and admitted that I was wrong, thus using my post in support of your argument is pointless. I already said it, but I'll say it again: the only direction work has is + or -; as per the prevailing definition, that makes it a scalar quantity.
This is because the dot product is simply a projection: just as a shadow is a 2D flattening of a 3D object, so the dot product is a scalar projection of one vector onto another. You're simply measuring the size of the shadow it casts. The fact you use the cosine operator reduces the domain of direction from all real numbers to a domain of n * pi. In short, you can only call it a vector if the domain of direction includes all real numbers.
This is because the dot product is simply a projection: just as a shadow is a 2D flattening of a 3D object, so the dot product is a scalar projection of one vector onto another. You're simply measuring the size of the shadow it casts. The fact you use the cosine operator reduces the domain of direction from all real numbers to a domain of n * pi. In short, you can only call it a vector if the domain of direction includes all real numbers.