What is the projection of #<-3,5,-9 ># onto #<2,-1,4 >#?

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Answer 1 · 2017-02-14T10:46:09

The vector projection is #=-47/21<2,-1,4>#
The scalar projection is #=-47/sqrt21#

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

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

The dot product is

#veca.vecb= <2,-1,4>.<-3,5,-9>=-6-5-36=-47#

The modulus of #veca# is

#=||<2,-1,4>|| =sqrt(4+1+16)=sqrt21#

The vector projection is

#=-47/21<2,-1,4>#

The scalar projection is

#=(veca.vecb)/||veca||=-47/sqrt21#