What is the projection of #<8,-5,3 ># onto #<7,6,0 >#?

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Answer 1 · 2018-02-05T07:00:23

The projection is #=26/85<7,6,0> #

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

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

#veca= <7,6,0>#

#vecb= <8,-5,3>#

The dot product is

#veca.vecb= <7,6,0> . <8, -5,3> = (7)*(8)+(6)*(-5)+(0)*(3)#

#=56-30+0=26#

The modulus of #veca# is

#||veca|| = ||<7,6,0>|| = sqrt((7)^2+(6)^2+(0)^2)#

#= sqrt(49+36+0)=sqrt(85)#

Therefore,

#proj_(veca)vecb=(26)/(sqrt85)^2* <7,6,0>#

#=26/85<7,6,0>#