Section 12.4: Cross Product

Suppose that \(\mathbf{a} \ne \mathbf{0}\). (a) If \(\mathbf{a} \cdot \mathbf{b} = \mathbf{a} \cdot \mathbf{c}\), does it follow that \(\mathbf{b} = \mathbf{c}\)? (b) If \(\mathbf{a} \times \mathbf{b} = \mathbf{a} \times \mathbf{c}\), does it follow that \(\mathbf{b} = \mathbf{c}\)? (c) If \(\mathbf{a} \cdot \mathbf{b} = \mathbf{a} \cdot \mathbf{c}\) and \(\mathbf{a} \times \mathbf{b} = \mathbf{a} \times \mathbf{c}\), does it follow that \(\mathbf{b} = \mathbf{c}\)?