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 $=(veca.vecb)/(||veca||)=50/sqrt59$

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