Dear Dean,
What does {1,2,3} represent here? should the vector start at {0,0,0} and point to {1,2,3} ? Where does the vector {4,5,6} start? also at {0,0,0} ?
vec = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
Graphics3D[Arrow[{{0, 0, 0}, #} & /@ vec]]
I'm not sure if you want this exactly.
Regards.
Sander