Vectors in Space · Challenge problem

Vectors $\mathbf a, \mathbf b, \mathbf c$ in space each have length $2$, and $\mathbf a \cdot \mathbf b = 1$, $\mathbf b \cdot \mathbf c = 2$, $\mathbf c \cdot \mathbf a = -1$. Find the volume of the parallelepiped they span.