Question

The sine of the angle between the vectors $\overline{a}=3\hat{i}+\hat{j}+\hat{k},\overline{b}=2\hat{i}-2\hat{j}+\hat{k}$ is

• A. $\sqrt{\frac{74}{99}}$
• B. $\sqrt{\frac{25}{99}}$
• C. $\sqrt{\frac{37}{99}}$
• D. $\frac{5}{\sqrt{41}}$

Answer 1

The correct option is A $\sqrt{\frac{74}{99}}$

$a.b=|a|.|b|cos\theta$
Applying this we get
$6-2+1=\sqrt{11.9}.cos\theta$
$cos\theta =\frac{5}{\sqrt{99}}$
Hence
$sin\theta =\sqrt{1-\frac{25}{99}}$
$=\sqrt{\frac{74}{99}}$