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Vector equation of a St Line

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THEVECTOREQUATIONOFASTRAIGHTLINELeti,andj,beunitvectorsinthexandydirectionsrespectively.Letrbythepositionvectorofanypointontheliney=mx+cThegeneralvectorequationofastraightlinethencanbewrittenas:,r=oc+ut,(1)whereuisavectorparalleltoy=mx+candtisascalarmultiplier.Letpbethepointony=mx+catwhichx=1.Thenphascoordinates(1,m+c)opandoccanbeusedtofindvectorusince:op=oc+cp=oc+u,hence,u=op–oc.Butop=1i+(m+c)jandoc=cj,thus,u=1i+(m+c)j–cj=i,+mjhence,r=oc+ut=cj+(i,+mj)t=it+(c+mt)jHencer=it+(c+mt)j(2)

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Vectors and Straight lines

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Noel Platt
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