Question

If $\theta$ is the angle between two lines whose d.rs are $-1,-2,1$ and $-2,1,1$, then $\tan \theta =$

• A. $\sqrt{35}$
• B. $\frac{1}{\sqrt{35}}$
• C. $\frac{1}{6}$
• D. $5$

Answer 1

The correct option is A $\sqrt{35}$

Given dr's are $-1,-2,1$ and $-2,1,1$

Then, $\cos \theta =\frac{2-2+1}{\sqrt{1+4+1}\sqrt{4+1+1}}$
$\therefore \cos \theta =\frac{1}{6}$
We know, $\tan \theta =\sqrt{(\sec \theta {)}^2-1}$
$\therefore \tan \theta =\sqrt{35}$