What is the projection of #< 2 , -6, 0># onto #< -1, -4 , 6 >#?

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Answer 1 · 2017-02-01T09:07:31

#=11/530sqrt530<-1, -4, 6> =0.4778<-1, -4, 6>#, nearly..

The unit vector in the direction #vecb=<-1, -4, 6># is

#1/|vecb|vecb#

#=1/sqrt((-1)^2+(-4)^2+6^2)vecb#

#=1/sqrt53vecb#

The projection #vecc#of #veca = <2, -6, 0># onto #vecb# is of

length ( modulus )

#|veca.vecb| / | veca |=22/sqrt40=11/10sqrt10#.

Now, the projected vector

#vecc=11/10sqrt10# (unit vector in the direction #vecb#)

#=11/10sqrt10(1/sqrt53<-1, -4, 6>)#

#=11/530sqrt530<-1, -4, 6>#