Section 12.3: Dot Product

Determine whether the given vectors are orthogonal, parallel, or neither. (a) \(\mathbf{a} = \langle 9, 3 \rangle, \mathbf{b} = \langle -2, 6 \rangle\) (b) \(\mathbf{a} = \langle 4, 5, -2 \rangle, \mathbf{b} = \langle 3, -1, 5 \rangle\) (c) \(\mathbf{a} = -8\mathbf{i} + 12\mathbf{j} + 4\mathbf{k}, \mathbf{b} = 6\mathbf{i} - 9\mathbf{j} - 3\mathbf{k}\) (d) \(\mathbf{a} = 3\mathbf{i} - \mathbf{j} + 3\mathbf{k}, \mathbf{b} = 5\mathbf{i} + 9\mathbf{j} - 2\mathbf{k}\)