What is the projection of <-3,0,1> onto <1,2,-4>?

1 Answer
Oct 28, 2017

The projection is = <-1/3,-2/3,4/3>

Explanation:

The projection of vecb onto veca is

proj_(veca)vecb=(veca.vecb)/(||veca||)^2veca

Here,

veca= <1,2,-4>

vecb= <-3,0,1>

The dot product is

veca.vecb=<1,2,-4>.<-3,0,1>=(1)xx(-3)+(2)xx(0)+(-4)xx(1)=-3-4=-7

The modulus of veca is

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

Therefore,

The projection is

proj_(veca)vecb = (-7)/(21)<1,2,-4> =-1/3<1,2,-4>

= <-1/3,-2/3,4/3>