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I have the following code

o = {Red, PointSize[.03], Point[orig = {0, 0, 0}]};
u = {2, a, -1};
v = {3, 1, -2};
w = {2 a - 1, -2, 4};
Solve[Dot[u, v] == Dot[u + v, v + w], a]
a = a /. Flatten[%];
Graphics3D[{Text[Style["u", Large, Bold, Red], Offset[{-50, -30, 0}, u]],
  Text[Style["v", Large, Bold, Red], Offset[{-50, -30, 0}, v]],
  Text[Style["w", Large, Bold, Red], Offset[{-50, -30, 0}, w]],
  Arrow[{orig, (u)}],Arrow[{orig, (v)}],Arrow[{orig, (w)}],o},
  Axes -> True,AxesOrigin -> Automatic]

On my screen appears the following warning me stating the following: Too many arguments given

If I eliminate the error, my result does not appear. but if I disregard, it's OK.

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I think you've used the Offset command rather than just putting in the offset coordinates. I've had to change the offset coordinates from {-50, -30} to get the offset in the right ballpark.

a =.
o = {Red, PointSize[.03], Point[orig = {0, 0, 0}]};
u = {2, a, -1};
v = {3, 1, -2};
w = {2 a - 1, -2, 4};
Solve[Dot[u, v] == Dot[u + v, v + w], a]
a = a /. Flatten[%];
Graphics3D[{
  Text[Style["u", Large, Bold, Red], u, {-.50, -.30}], 
  Text[Style["v", Large, Bold, Red], v, {-.50, -.30}], 
  Text[Style["w", Large, Bold, Red], w, {-.50, -.30}],
  Arrow[{orig, (u)}], Arrow[{orig, (v)}], Arrow[{orig, (w)}], o}, 
 Axes -> True, AxesOrigin -> Automatic]

Labeled vectors

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