1. The problem statement, all variables and given/known data http://mathwiki.ucdavis.edu/Core/Ca.../The_Unit_Tangent_and_the_Unit_Normal_Vectors In the link, I cant understand that why the Principal Unit Normal Vector is defined by N(t) = T'(t) / | T'(t) | ,can someone explain.... 2. Relevant equations 3. The attempt at a solution Since tangent vector is normal to principal normal vector, why the N(t) shouldn't be -1 / ( T'(t) / | T'(t) | ) , since we know that if two vectors ( A and B) are prependicular to each other, then A multiply by B will get -1, so, N(t) shouldn't be -1 / ( T'(t) / | T'(t) | ), am i right? why we must differentiate it?