Question

The unit vector perpendicular to $3\mathbf{i} + 2\mathbf{j} - \mathbf{k}$ and $12\mathbf{i} + 5\mathbf{j} - 5\mathbf{k},$ is

• A. $\frac{5\mathbf{i} - 3\mathbf{j} + 9\mathbf{k}}{\sqrt{115}}$
• B. $\frac{5\mathbf{i} + 3\mathbf{j} - 9\mathbf{k}}{\sqrt{115}}$
• C. $\frac{- 5\mathbf{i} + 3\mathbf{j} - 9\mathbf{k}}{\sqrt{115}}$
• D. $\frac{5\mathbf{i} + 3\mathbf{j} + 9\mathbf{k}}{\sqrt{115}}$

Answer 1

Answer: (C)

$\frac{- 5\mathbf{i} + 3\mathbf{j} - 9\mathbf{k}}{\sqrt{115}}$

Answer 2

\mathbf{i} & \mathbf{j} & \mathbf{k} \\ 3 & 2 & - 1 \\ 12 & 5 & - 5 \end{matrix} \right| = - 5\mathbf{i} + 3\mathbf{j} - 9\mathbf{k}.$$ Unit vector along $\mathbf{a} \times \mathbf{b} = \frac{- 5\mathbf{i} + 3\mathbf{j} - 9\mathbf{k}}{\sqrt{115}}.$