What is the projection of #<-7 , -7, 1 ># onto #< 4, 0, -2 >#?

Question

1008 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-02T10:54:07

The vector projection is #=<-6,0,3>#
The scalar projection is #=-3sqrt5#

The vector projection of #vecu# onto #vecv# is

#=(vecu.vecv)/(||vecv||^2)vecv#

The dot product is

#vecu.vecv=<-7,-7,1>,<4,0,-2> =-28+0-2=-30#

The modulus of #vecv# is

#=||vecv||=||vecv||= ||<4,0,-2||#

#=sqrt(16+0+4)=sqrt20#

The vector projection is

#=-30/20<4,0,-2>#

#= <-6,0,3>#

The scalar projection is

#=(vecu.vecv)/(||vecv||)#

#=-30/sqrt20=-15/sqrt5=-3sqrt5#