What is the projection of #< -3 , 1 ,3 ># onto #< 4, 9, 1>#?

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Answer 1 · 2017-12-08T08:10:20

The vectors are perpendicular, no projection is possible.

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

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

Here,

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

#vecu = <4,9,1>#

The dot product is

#vecu.vecv =<-3,1,3> . <4,9,1> #

#=(4*-3)+(9*1)+(3*1) =-12+9+3=0#

As the dot product is #=0#, the #2# vectors #vecu# and #vecv# are perpendicular, there is no projection.