What is the projection of #(3i - j - 2k)# onto # (3i – 4j + 4k)#?

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Answer 1 · 2018-01-16T06:15:22

The projection is #=5/41<3, -4,4>#

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

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

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

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

The dot product is

#veca.vecb =<3,-4,4>. <3,-1,-2> #

# = (3)*(3)+(-4) *(-1)+(4)*(-2)=9+4-8=5 #

The modulus of #veca# is

#=||veca||=||<3,-4,4>|| =sqrt((3)^2+(-4)^2+(4)^2)=sqrt41#

Therefore,

#proj_(veca)vecb=5/41<3, -4,4>#