n = 4;
positions = RandomReal[{-10, 10}, {n, 3}];
vectors = RandomPoint[Sphere[], n];
lengths = RandomReal[{0, 20}, n];
lines = MapThread[
   Line[{#1, #1 + #2*#3}] &, {positions, lengths, vectors}];
Graphics3D[{Thick, Red, lines}]