What is the projection of #<-2,4,2 ># onto #<1,8,-3 >#?

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Answer 1 · 2017-10-14T09:11:24

The projection is #=12/37<1,8,-3>#

Let the vectors be

#vecu=<-2,4,2>#

and

#vecv=<1,8,-3>#

The projection of #vecu# onto #vecv# is

#proj_(vecv)vecu=(vecu.vecv)/(||vecv||^2)vecv#

#=(<-2,4,2>.<1,8,-3>)/(||<1,8,-3>||^2)<1,8,-3>#

#=(-2+32-6)/(1+64+9)<1,8,-3>#

#=24/74<1,8,-3>#

#=12/37<1,8,-3>#