Section 12 1 Worksheet 6 VECTOR VALUED FUNCTIONS HW 12 1 9 13 17 21 24 27 31 35 39 41 49 53 55 57 59 63 67 Def A space curve or parameterized curve is A special type of space curve that we have already seen is Def A vector valued function is a function of the form To plot vector valued functions we treat the vectors as points the terminal points of the vectors in standard position Goals 1 2 HINT to Plot find relationships between x y z Ex 1 Sketch the curve traced out by the vector valued function r t h1 t t2 i Include the orientation of the curve NOTE As before parameterizations of a curve are 1 Ex 2a Sketch the curve traced out by r t h2 cos t 0 2 sin ti Include the orientation of the curve Ex 2b Sketch the curve traced out by r t h2 cos t t 2 sin ti Include the orientation of the curve This curve is called a Ex 3a Sketch the curve traced out by r t ht sin t t2 i Include the orientation of the curve 2 Ex 3b Sketch the curve traced out by r t ht2 t4 0i In the plane to parameterize the graph of y f x from left to right use NOTES 1 If r t traces out a curve then r t replace t by t will trace the same curve 2 If r t traces out a curve then r 2t replace t by 2t will trace the same curve 3 If r t traces out a curve then r t c replace t by t c will trace the same curve Ex 4a Find two parameterizations for y x3 for 0 x 2 one from left to right and one from right to left 3 In general to parameterize a curve try setting t equal to one of x y or z 2 2 If circles ellipses are present e g xa2 yb2 then try x a cos t and y b sin t 2 2 Ex 4b Find two parameterizations for the ellipse x4 y9 1 NOTE DO not use as a parameter BAD BOOK Ex 5 Find a vector valued function to represent the curve of intersection between surfaces given by x2 y 2 z 2 16 and x y 4 Assume x y and z are all positive Ex 6 Use a vector valued function to represent the curve of intersection between the surfaces given by z x2 y 2 and x2 y 2 1 4