>>14302680Your question isn't coherently written, it would aid your learning if you for yourself isolated what exactly is it that I don't understand, and if you phrase your own question well enough most times you can answer it yourself. Figure out what you don't understand better.
Vectors are twodimensional or more, they don't just have a length, they have direction. [0,1] is not the same as [1,0] or [-1,0] or [sqrt(0.5),sqrt(0.5)] , you apply a transformation to an object to maintain the information you're working with. Otherwise it's like a derivative, you lose information. Derivating then integrating, you don't have the information you started out with. Same thing with vectors. Take the length of a vector, then you lose the direction. You don't know what way it will be pointing. Take the length of vector [1,1,1] , it's sqrt(3) , and then what? You just have a length. It doesn't tell you anything. It's not a vector. If you want a new vector, you multiply that length onto a vector with the direction you want of length 1, say [1,0,0], so the new vector with the same magnitude but a different direction is [sqrt(3),0,0]. The important concept here is dimension. Taking the length of something removes all dimensions because length is onedimensional. It's scalar. Use that scalar on an object with the correct dimension of unit length with the angles you want.
