Let vectors $\mathbf{a}, \mathbf{b}, \mathbf{c}$ be such that
$$
\mathbf{a} = \hat{i} + 2\hat{j} - \hat{k}, \quad \mathbf{b} = 2\hat{i} - \hat{j} + \hat{k}, \quad \mathbf{c} = \hat{i} + \hat{j} + \hat{k}
$$
Then the volume of the parallelepiped formed by these vectors is:
Show Hint
The volume of a parallelepiped is found using the scalar triple product:
\[
V = | \mathbf{a} \cdot (\mathbf{b} \times \mathbf{c}) |
\]
Ensure correct determinant calculation and sign handling.