Question

If $\alpha$ is the angle between two vectors $\bar{P}=3 \hat{i}+4 \hat{j}-\hat{k}$ and $\bar{q}=2 \hat{i}-\hat{j}+\hat{k}$ then, $\sin (\alpha)=$

• A. $\sqrt{145 / 156}$
• B. $\sqrt{135 / 156}$
• C. $\sqrt{155 / 156}$
• D. $\sqrt{165 / 156}$

Answer 1

Answer: (C)

If $\alpha$ is an acute angle between vectors $p$ and $q$, then
$\text{Sin} \alpha=\frac{|p \times q|}{|p| q \mid}=\frac{\sqrt{(4-1)^{2}+(-3-2)^{2}+(-3-8)^{2}}}{\sqrt{9+16+1} \sqrt{4+1+1}}$
$=\frac{\sqrt{9+25+121}}{\sqrt{156}}$
$=\sqrt{\frac{155}{156}}$