Math 151 Section 1 3 Vector Functions and Parametric Curves Parametric Curve Let x be functions of t where t is a parameter As t varies over its domain the collection of points x y x t y t defines a parametric curve Example Sketch the given parametric curves x t t 3 A y t 2t 1 B C x t 1 2t y t 2 3t x t t 1 y t t 2 4 for 3 t 3 Math 151 D E x t t y t 1 t x t 2sin y t 3cos Math 151 Vector Functions For each value of t consider the point x y x t y t on the parametric curve to be the terminal point of a vector r t x t y t originating from the origin r defines a vector function Example Sketch the given curves as defined by the vector functions Include the direction of the curve as t increases A r t t 3 2t 1 B r t 2 cost 1 sin t Math 151 Vector Equation of a Line The vector equation of a line passing through the point r0 x0 y0 and parallel to the vector v v1 v2 is given by r t r0 tv The corresponding parametric equations of the line are given by x t x0 tv1 y t y0 tv2 Example Find a vector function of the line parallel to the vector 1 4 and passing through the point 1 5 Example Find parametric equations for the line with slope 4 and passing through the point 2 5 3 Math 151 Example An object is moving in the xy plane and its position after t seconds is given by r t t 4 t 2 2 A What is the position of the object at time t 2 B At what time does the object reach the point 7 11 C Does the object pass through the point 9 20 D Eliminate the parameter to find the Cartesian equation
View Full Document
Unlocking...