Question

The site of the angle between the two vectors $3\mathbf{i} + 2\mathbf{j} - \mathbf{k}$ and $12\mathbf{i} + 5\mathbf{j} - 5\mathbf{k}$ will be

• A. $\frac{\sqrt{115}}{\sqrt{14}\sqrt{194}}$
• B. $\frac{51}{\sqrt{14}\sqrt{144}}$
• C. $\frac{\sqrt{64}}{\sqrt{14}\sqrt{194}}$
• D. None of these

Answer 1

Answer: (A)

$\frac{\sqrt{115}}{\sqrt{14}\sqrt{194}}$

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}$$ $\Rightarrow \sin\theta = \frac{\sqrt{25 + 9 + 81}}{\sqrt{14}.\sqrt{194}} = \frac{\sqrt{115}}{\sqrt{14}.\sqrt{194}}$.