so i've been doing vectors for quite some time now and eventhough i excel at vectors and calculus 3, what exactly is the point of having unit vectors. Why can't we just right them as normal vectors especially when i get to binormals and stuff, they always want unit vectors. Also, if you take the cross product of two unit vectors, do you end up with a unit vector. if not, can you please explain why not
unit vectors serve as a basis wrt which other vectors can be expressed. They are usually used as a unit orthogonal (orthonormal) basis ( a.a=1, a.b=0) , in which case the length of any vector is the sum of the squares of it's components.