Lattices

The given primitive vectors represent a body-centered cubic (BCC) lattice. To verify this, let's examine the structure.
The primitive vectors are given as:

The BCC lattice is characterized by one atom at the corner and one at the center of the unit cell. To calculate the volume of the primitive cell, we can use the scalar triple product:

First, calculate the cross product :

Now, calculate the dot product with :

Thus, the volume of the primitive cell is . Therefore, the correct answer is option (A).