The angle between the lines whose direction c | vedclass

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(C) Given,direction cosines of line $1$ are $(l_{1}, m_{1}, n_{1}) = \left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{\sqrt{3}}{2}\right)$.Direction cosin

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$\frac{\pi}{3}$

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(C) Given,direction cosines of line $1$ are $(l_{1}, m_{1}, n_{1}) = \left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{\sqrt{3}}{2}ight)$.Direction cosines of line $2$ are $(l_{2}, m_{2}, n_{2}) = \left(\frac{\sqrt{3}}{4}, \frac{1}{4}, -\frac{\sqrt{3}}{2}ight)$.The angle $	heta$ between two lines is given by $\cos 	heta = |l_{1}l_{2} + m_{1}m_{2} + n_{1}n_{2}|$.Substituting the values:$\cos 	heta = \left|\left(\frac{\sqrt{3}}{4} 	imes \frac{\sqrt{3}}{4}ight) + \left(\frac{1}{4} 	imes \frac{1}{4}ight) + \left(\frac{\sqrt{3}}{2} 	imes -\frac{\sqrt{3}}{2}ight)ight|$$\cos 	heta = \left|\frac{3}{16} + \frac{1}{16} - \frac{3}{4}ight|$$\cos 	heta = \left|\frac{3 + 1 - 12}{16}ight| = \left|-\frac{8}{16}ight| = \left|-\frac{1}{2}ight| = \frac{1}{2}$.Since $\cos 	heta = \frac{1}{2}$,we have $	heta = \frac{\pi}{3}$.

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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