What is the projection of #<-5,2,8># onto #<4,-6,3 >#?

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Answer 1 · 2018-01-26T10:55:13

The projection is #=-8/sqrt61<4, -6,3>#

The vector projection of #vecb# onto #veca# is

#proj_(veca)vecb=(veca.vecb)/(||veca||)^2veca#

#veca=<4,-6,3>#

#vecb= <-5, 2,8>#

The dot product is

#veca.vecb =<4,-6,3>. <-5,2,8> #

# = (4)*(-5)+(-6) *(2)+(3)*(8)=-20-12+24=-8 #

The modulus of #veca# is

#=||veca||=||<4,-6,3>|| =sqrt((4)^2+(-6)^2+(3)^2)=sqrt61#

Therefore,

#proj_(veca)vecb=-8/sqrt61<4, -6,3>#