Your question is somewhat twisted up. We would be justified in simply asking you to correct the question. But I think I know what you're talking about, so I'll try to answer it.
A horizontal vector is one that's oriented at an angle of zero degrees, not 45 degrees. I think what you want is the horizontal component of the vector that you're describing.
Its horizontal component is 100 cos(45) = 100 / √2 = 70.71 units.
