What is the projection of # <3,1,5># onto #<2,3,1>#?

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Answer 1 · 2018-01-20T06:45:32

The vector projection is #= <2, 3, 1>#

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

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

#veca=<2,3,1>#

#vecb= <3, 1,5>#

The dot product is

#veca.vecb =<3,1,5>. <2,3,1> #

# = (3)*(2)+(1) *(3)+(5)*(1)=6+3+5=14 #

The modulus of #veca# is

#=||veca||=||<2,3,1>|| =sqrt((2)^2+(3)^2+(1)^2)=sqrt14#

Therefore,

#proj_(veca)vecb=14/14<2, 3,1>#