What is the projection of $<8,-1,6 >$ onto $<-1,5,-3 >$ ?

Question

1480 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-21T19:21:34

The vector projection is $〈-31/35,-31/7,93/35〉$

Let $vecb=〈8,-1,6〉$

and $veca=〈-1,5,-3〉$

Then the vector projection of $vecb$ onto $veca$ is
$=(veca.vecb)/(∣veca∣)^2*veca$
where the dot product is $veca.vecb$

dot product $(8*-1)+(-1*5)+(6*-3) =-8-5-18=-31$

and $(∣veca∣)^2=(1+25+9)=35$

so the projection is $-31/35〈-1,5,-3〉 =〈-31/35,-31/7,93/35〉$

What is the projection of <8,-1,6 ><8,-1,6 > onto <-1,5,-3 ><-1,5,-3 >?