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

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Aicharya · Accepted Answer

Given that, $ l_1=\frac{\sqrt{3}}{4}, m_1=\frac{1}{4} 	ext { and } n_1=\frac{\sqrt{3}}{2} $ and $l_2=\frac{\sqrt{3}}{4}, m_2=\frac{1}{4}$ and $n_2=\frac{-\sqrt{3}}{2}$ $ \begin{aligned} 	herefore \cos 	heta & =\left|l_1 l_2+m_1 m_2+n_1 n_2ight| \ & =\left|\frac{\sqrt{3}}{4} 	imes \frac{\sqrt{3}}{4}+\frac{1}{4} 	imes \frac{1}{4}+\frac{\sqrt{3}}{2} 	imes\left(\frac{-\sqrt{3}}{2}ight)ight| \ & =\left|\frac{3}{16}+\frac{1}{16}-\frac{3}{4}ight|=\left|-\frac{2}{4}ight|=\frac{1}{2} \ \Rightarrow \quad 	heta & =\frac{\pi}{3} \end{aligned} $

The angle between the lines whose direction cosines are $\left(\frac{\sqrt{3}}{4}, \frac{1}{4},…

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