What is the projection of #<-4,8,9 ># onto #<8,1,-1 >#?

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Answer 1 · 2017-12-05T18:09:07

The projection is #=<-4,-1/2, 1/2>#

The vector projection of #vecv# onto #vecu# is

#proj_uv= (vec u. vecv ) /(||vecu||)^2*vecu#

Here,

#vecv= < -4,8,9> # and

#vecu = <8,1,-1>#

The dot product is

#vecu.vecv =<-4,8,9> . <8,1,-1> #

#=(-4*8)+(8*1)+(9*-1) =-32+8-9=-33#

The magnitude of #vecu# is

#=||<8,1,-1 >|| = sqrt((8)^2+(1)^2+(-1)^2)#

#=sqrt(64+1+1)=sqrt66#

The vector projection is

#proj_uv=-33/66* <8,1,-1> = <-4,-1/2, 1/2>#