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Answer 1 · 2017-03-30T14:25:14

The vector projection is #=<2/9,4/9,4/9>#
The scalar projection is #=2/3#

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

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

#vecb=<1,2,2>#

#veca=<2,-1,1>#

The dot product is

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

The modulus of #vecb# is

#=||<1,2,2>||=sqrt(1+4+4)=sqrt9=3#

The vector projection is

#=2/9*<1,2,2>#

The scalar projection is

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

#=2/3#