What is the projection of #(i -2j + 3k)# onto # ( 2i+j+2k)#?

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Answer 1 · 2018-07-08T08:58:21

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

The projection of #vecb# onto #veca# is

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

The vectors are

#veca= <2,1,1 >#

and

#vecb= <1,-2,3>#

The dot product is

#veca.vecb= <2,1,1 > . <1,-2,3> #

#= (2xx1)+(1xx(-2))+ 1xx3=2-2+3=3#

The magnitude of #veca # is

#||veca|| = <2,1,1> = sqrt(2^2+1^2+1^2)=sqrt6#

Therefore,

#proj_(veca)vecb=(3)/(6)*<2,1,1 >#

#= <1,1/2,1/2>#