Question

The angle between the lines whose direction cosines are $\left(\frac{\sqrt{3}}{4},\frac{1}{4},\frac{\sqrt{3}}{2}\right)$ and $\left(\frac{\sqrt{3}}{4},\frac{1}{4},\frac{-\sqrt{3}}{2}\right)$ is

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

Answer 1

Answer: (C)

$\cos \theta =\left|\frac{\sqrt{3}}{4}\times \frac{\sqrt{3}}{4}+\frac{1}{4}\times \frac{1}{4}-\frac{\sqrt{3}}{2}\times \frac{\sqrt{3}}{2}\right|=\left(\frac{-1}{2}\right),\theta$
$=\frac{\pi }{3}$