Exercise 13

State whether each expression is meaningful. If not, explain why. If so, state whether it is a vector or a scalar. (a) \(\mathbf{a} \cdot (\mathbf{b} \times \mathbf{c})\) (b) \(\mathbf{a} \times (\mathbf{b} \cdot \mathbf{c})\) (c) \(\mathbf{a} \times (\mathbf{b} \times \mathbf{c})\) (d) \(\mathbf{a} \cdot (\mathbf{b} \cdot \mathbf{c})\) (e) \((\mathbf{a} \cdot \mathbf{b}) \times (\mathbf{c} \cdot \mathbf{d})\) (f) \((\mathbf{a} \times \mathbf{b}) \cdot (\mathbf{c} \times \mathbf{d})\)