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

1 Answer
Oct 21, 2016

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

Explanation:

Let vecb=〈6,0,3〉

and veca=〈2,5,-7〉

The dot product is veca.vecb=(6*2+5*0+3*-7)=12-21=-9

∣veca∣^2= (4+25+49)=78

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