Find the following expressions if $\mathbf{a} = 2\mathbf{i} - 5\mathbf{k}$, $\mathbf{b} = \mathbf{i} +\mathbf{j} - 5\mathbf{k}$, and $\mathbf{c} = 4\mathbf{i} +2\mathbf{j} + 2\mathbf{k}$.

---

1. $\space \mathbf{a} \cdot \mathbf{b} =$

2. $\space \mathbf{a} \cdot \mathbf{c} =$

3. $\space \mathbf{b} \cdot \mathbf{c} =$

---