Corrolate points of two parallel vectors

Hello there. I have two parallel vectors of xy- coordinates and i try to assign each point of the first vector to the point of the second vector. i think you have to create an orthogonal vector to the first and then just pick the crossing of the orgthogonal and the second vector. i have v1=[x1;y1] and v2=[x2;y2]. i know i have to do this with the scalar product but how to i make the loop over each point?

if true
  % code
v1=[x1;y1]
v2=[x2;y2]
for i=1:length(v1)
orth=...dot(...)/dot(...)*v1 %???
end