Well, you get the equation for the line between 2 points like this:
r1 = [x1,y1,z1]; % First point
r2 = [x2,y2,z2]; % second point
e1_2_2 = r2-r1; % array pointing from r1 towards r2 - to unit vector along line
l1_2_2 = norm(e1_2_2); % length between points
e1_2_2 = e1_2_2/l1_2_2; % unit vector along line
% Then the equation for the line between the points are
r_on_line = r1 + l*e1_2_2; % Where 0<= l <= l1_2_2
HTH
