What is the projection of <6,0,3 ><6,0,3> onto <2,5,-7 ><2,5,7>?

1 Answer
Oct 21, 2016

The vector projection is 〈-9/39,-45/78,63/78〉939,4578,6378

Explanation:

Let vecb=〈6,0,3〉b=6,0,3

and veca=〈2,5,-7〉a=2,5,7

The dot product is veca.vecb=(6*2+5*0+3*-7)=12-21=-9a.b=(62+50+37)=1221=9

∣veca∣^2= (4+25+49)=78a2=(4+25+49)=78

So the projection is
(veca.vecb)veca / (∣veca∣^2)=-9/78 〈2,5,-7〉(a.b)aa2=9782,5,7