Section 12.3: Dot Product

Which of the following expressions are meaningful? Which are meaningless? Explain. (a) \((\mathbf{a} \cdot \mathbf{b}) \cdot \mathbf{c}\) (b) \((\mathbf{a} \cdot \mathbf{b})\mathbf{c}\) (c) \(|\mathbf{a}|(\mathbf{b} \cdot \mathbf{c})\) (d) \(\mathbf{a} \cdot (\mathbf{b} + \mathbf{c})\) (e) \(\mathbf{a} \cdot \mathbf{b} + \mathbf{c}\) (f) \(|\mathbf{a}| \cdot (\mathbf{b} + \mathbf{c})\)