Question

If $\overset{\rightarrow}{A} = 3\mathbf{i} + \mathbf{j} + 2\mathbf{k}$ and $\overset{\rightarrow}{B} = 2\mathbf{i} - 2\mathbf{j} + 4\mathbf{k}$ and θ is the angle between $\overset{\rightarrow}{A}$ and $\overset{\rightarrow}{B},$ then the value of $\sin\theta$ is

• A. $\frac{2}{\sqrt{7}}$
• B. $\sqrt{\frac{2}{7}}$
• C. $\frac{4}{\sqrt{7}}$
• D. $\frac{3}{\sqrt{7}}$

Answer 1

Answer: (A)

$\frac{2}{\sqrt{7}}$

Answer 2

$\cos\theta = \frac{\overset{\rightarrow}{A}.\overset{\rightarrow}{B}}{|\overset{\rightarrow}{A}||\overset{\rightarrow}{B}|} = \frac{6 - 2 + 8}{\sqrt{14} \times \sqrt{24}}$

$\cos\theta = \frac{12}{\sqrt{14} \times \sqrt{24}} = \sqrt{\frac{3}{7}}$, $\therefore\sin\theta = \frac{2}{\sqrt{7}}$.