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

1 Answer
Oct 21, 2016

Answer:

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〉#