What is the projection of # (4 i + 4 j + 2 k)# onto #(- 5 i + 4 j - 5 k)#?

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Answer 1 · 2017-12-27T17:31:30

The projection is #=-7/33 <-5,4,-5>#

The vector projection of #vecb# onto #veca#

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

Here,

#vecb= <4,4,2>#

#veca= <-5,4,-5>#

The dot product is

#veca.vecb= <4,4,2>. <-5,4,-5> =(4*-5)+(4*4)+(2*-5)= -20+16-10=-14#

The modulus of #vecb# is

#||veca||=sqrt((-5)^2+(4)^2+(-5)^2)=sqrt(66)#

Therefore,

#proj_(veca)vecb=(-14)/(66)*<-5,4,-5>#

# =-7/33<-5,4,-5>#