Let $\vec{A} = \hat{i} - \hat{j} + \hat{k}$ and $\vec{C} = -\hat{i} - \hat{j}$ be two vectors. Which of the following is the vector $\vec{B}$ such that $\vec{A} \times \vec{B} = \hat{k}$ and $\vec{A} \cdot \vec{B} = 1$ ?