What is the projection of #<3 ,-4, 7 ># onto #< -1 , 0, -2 >#?

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Answer 1 · 2018-04-23T09:48:51

Projection of #veca=<3,-4,7># onto #vecb<-1,0,-2># is #<-51/74,34/37,-119/74>#

Projection of #veca=<x_1,y_1,z_1># onto #vecb=<x_2,y_2,z_2># is #(veca*vecb)/|veca|^2*veca#

Hence for projection of #veca=<3,-4,7># onto #vecb<-1,0,-2>#

as #veca*vecb= 3xx(-1)+(-4)xx0+7xx(-2)=-17#

#|veca|^2=3^2+(-4)^2+7^2=74#

Projection of #veca=<3,-4,7># onto #vecb<-1,0,-2># is

#-17/74<3,-4,7>=<-51/74,68/74,-119/74># or #<-51/74,34/37,-119/74>#