Hi

The parametrization of the segment line limited by O(0,0,0) and I(1,1,0) isr(t) = ti+ tj, for t between 0 and 1

Take any point M (x,y,z) inside the segment line.OM=ris parallel toOI(1,1,0). This means that exists t such asOM= tOI.

On x axis this gives : x = t

On y axis : y = t

On z axis : z = 0

Therefore M(t,t,0) orOM= ti+ tj

I hope my explanation will be of help for you.