what is unit vector and where do we use it ? is there any example? i'm try to understand a definition designed by some else which has a unit vector, but i cant understand why the creator used unit vector
A unit vector is technically any vector whose length is one. Although vectors typically have direction and magnitude (length), unit vectors really only represent direction (since 1 leaves other numbers alone ;) ). The process of unitizing a vector will take its magnitude (length) and force it to 1. Almost all vectors that are generated by evaluating some geometric entity, such as retreving the a normal of a surface or the tangent of a curve, will be unitized and therefore equal 1. Using unit vectors instead of vectors of varying lengths is generally the preferred way to do any vector math, since it will only take into account the vector's direction, not its magnitued.