Drawing the volume generated by three vectors

Use Parallelepiped:

v1 = {1, 0, 0};
v2 = {0, 1, 0};
v3 = 1/2 {1, 1, 1};
Graphics3D[Parallelepiped[{0, 0, 0}, {v1, v2, v3}]]

To include the vectors in the drawing:

v = {{1, 0, 0}, {0, 1, 0}, 1/2 {1, 1, 1}};

ℛ = Parallelepiped[{0, 0, 0}, v];

Graphics3D[{
  {Opacity[0.7], ℛ},
  {Red, Arrowheads[0.05],
   Arrow[Tube[{{0, 0, 0}, #}, 0.01]] & /@ v}},
 Axes -> True,
 BoxRatios -> {1, 1, 1}]

The volume can be calculated multiple ways

{Volume[ℛ], RegionMeasure[ℛ], Integrate[1, {x, y, z} ∈ ℛ]}

(* {1/2, 1/2, 1/2} *)

SameQ @@ %

(* True *)