Let $$ABC$$ be a triangle in the $$xy$$ plane, where $$B$$ is at the origin $$(0,0)$$. Let $$BC$$ be produced to $$D$$ such that $$BC:CD=1:1$$, $$CA$$ be produced to $$E$$ such that $$CA:AE=1:2$$ and $$AB$$ be produced to $$F$$ such that $$AB:BF=1:3$$. Let $$G(32,24)$$ be the centroid of the triangle $$ABC$$ and $$K$$ be the centroid of the triangle $$DEF$$. Find the length $$GK$$.