Answer :

AL2006
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.