Lec_Notes_13.1-13.3 - MATH 214 Lecture Notes Section 13.1-13.3 1 Space curves A curve C in space can be represented by parametric equations x = f(t

Lec_Notes_13.1-13.3 - MATH 214 Lecture Notes Section...

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MATH 214 Lecture Notes Section 13.1-13.3 C.2Vector functionsDefinition: Suppose thatf, gandhare three functions defined on an intervalI. Letr(t) =f(t)i+g(t)j+h(t)k, tI.wherei,jandkare the unit coordinate vectors. Thenris called avector-valued functionor a vector function onI.Ifuandvare vector functions onIandcis a real number, thenu+vandcuare vectorfunctions onIsuch that for eachtI,(u+v)(t) =u(t) +v(t),(cu)(t) =c(u(t)).3Curves represented by vector functionsLetCbe a curve in space represented by parametric equationsx=f(t), y=g(t), z=h(t), tI.LetP= (f(t), g(t), h(t)) be a point on the curve. Then-→OPis called theposition vectorofP,and-→OP=f(t)i+g(t)j+h(t)k 1

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