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

1 Answer
Feb 14, 2016

vec c=<5/2,-5/2,0>

Explanation:

vec a=<5,0,-2>
vec b=<1,-1,0>
vec a*vec b=5*1+0*(-1)+0*(-2)=5
"dot product between vec a and vec b;"
|b|=sqrt(1^2+1^2+0^2)=sqrt 2
vec c=(vec a*vec b)/(|b|*|b|)*vec b
vec c=5/(sqrt 2*sqrt 2)*<1,-1,0>
vec c=5/2<1,-1,0>
vec c=<5/2,-5/2,0>