What is the projection of #<7,-5,6 ># onto #<-1,-3,7 >#?

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Answer 1 · 2017-02-13T10:52:24

The vector projection is #=50/59<-1,-3,7>#
The scalar projection is #=50/sqrt59#

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

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

The dot product is

#veca.vecb= <-1,-3,7>.<7,-5,6> =-7+15+42=50#

The modulus of #veca# is

#||<-1,-3,7>||=sqrt(1+9+49)=sqrt59#

The vector projection is #=50/59<-1,-3,7>#

The scalar projection is #=(veca.vecb)/(||veca||)=50/sqrt59#