I am considering curvature of a plane curve as covered in chapter 2 of Elementary Differential Geometry by Pressley. For a curve $c(t)$, we are considering the calculation of curvature and it is said that as we go from $c(t)$ to $c(t+dt)$, the curve moves away from the tangent at $c(t)$ by a distance of $(c(t+dt)-c(t)).n$ where $n$ is the normal to the tangent vector at $c(t)$. I just don't see how that expression gives that distance though. Is there some fact about vectors and dot products that I'm missing here? Any hints are much appreciated.