What is the projection of # <0,8,5># onto #<1,2,-4>#?

1 Answer
Apr 26, 2016

Answer:

#-4/sqrt(21)#

Explanation:

The projection of a vector #A# along a direction #theta# with itself is given as #|A|costheta#

Lets say here #A = <0,8,5>#
And #B = <1,2,-4>#

Their dot product is #|A| |B| costheta = 0+16-20 =-4#

So the projection is #(|A||B|costheta)/(|B|) = (-4)/sqrt(1^2+2^2+4^2) = -4/sqrt(21)#