= Parameterized Vector Geometry = [[Calculus/VectorGeometry|Vector geometry]] that is specific to [[Calculus/ParametricEquation|vector-valued parametric functions]]. <> ---- == Unit Tangent Vector == The tangent of a parametric curve ''r(t)'' is given by [[Calculus/Derivative|differentiating]] the curve. Most often, it is helpful to calculate the normalized vector. To calculate the unit tangent vector, try: {{attachment:t.svg}} ---- == Principal Unit Normal Vector == The '''principal normal vector''' is [[Calculus/Orthogonality|orthogonal]] to the tangent vector and points in the direction that a line is turning. Most often, it is helpful to calculate the normalized vector. To calculate the principal unit normal vector, try: {{attachment:n.svg}} ---- == Binormal Vector == The '''binormal vector''' is [[Calculus/Orthogonality|orthogonal]] to both the tangent vector and the principal normal vector. Naturally, this is calculated using the [[Calculus/VectorOperations#Cross_Product|cross product]]. By calculating this from unit vectors, the product will necessarily also be unit. ''B(t) = T(t) × N(t)'' ---- CategoryRicottone