The measure of the angle between the lines x | vedclass

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(B) The first line is given by $x = 1 + 1k, y = -1 + 2k, z = 3 + 2k$. Its direction ratios are $\vec{a} = (1, 2, 2)$.The second line is $\frac{x-1}{2}

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$\cos^{-1}(\sqrt{\frac{2}{3}})$

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(B) The first line is given by $x = 1 + 1k, y = -1 + 2k, z = 3 + 2k$. Its direction ratios are $\vec{a} = (1, 2, 2)$.The second line is $\frac{x-1}{2} = \frac{y-2}{1} = \frac{z-3}{1}$. Its direction ratios are $\vec{b} = (2, 1, 1)$.The angle $	heta$ between the lines is given by $\cos 	heta = \frac{|\vec{a} \cdot \vec{b}|}{|\vec{a}| |\vec{b}|}$.$\vec{a} \cdot \vec{b} = (1)(2) + (2)(1) + (2)(1) = 2 + 2 + 2 = 6$.$|\vec{a}| = \sqrt{1^2 + 2^2 + 2^2} = \sqrt{1 + 4 + 4} = \sqrt{9} = 3$.$|\vec{b}| = \sqrt{2^2 + 1^2 + 1^2} = \sqrt{4 + 1 + 1} = \sqrt{6}$.$\cos 	heta = \frac{6}{3 \cdot \sqrt{6}} = \frac{2}{\sqrt{6}} = \sqrt{\frac{4}{6}} = \sqrt{\frac{2}{3}}$.Therefore, $	heta = \cos^{-1}(\sqrt{\frac{2}{3}})$.

The measure of the angle between the lines $x = k + 1, y = 2k - 1, z = 2k + 3, k \in R$ and $\frac{x-1}{2} = \frac{y-2}{1} = \frac{z-3}{1}$ is

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