What is the projection of #< -3 , 1 ,3 ># onto #< 8 ,5 ,-3>#?

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Answer 1 · 2017-01-28T10:23:58

The vector projection is #=-2/7<8,5,-3>#
The scalar projection is #=-4/sqrt2#

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

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

The dot product is #veca.vecb=<-3,1,3>.<8,5,-3>#

#=-24+5-9=-28#

The modulus of #veca# is #||veca||=||<8,5,-3>||#

#=sqrt(64+25+9)=sqrt98#

The vector projection is #=-28/98<8,5,-3>#

#=-2/7<8,5,-3>#

The scalar projection is #=(veca.vecb)/(||veca||)#

#=-28/sqrt98=-4/sqrt2#