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

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

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