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 $<-51/74,34/37,-119/74>$

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