The angle between the lines with direction ra | vedclass

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(B) Let the direction ratios of the two lines be $\vec{a} = (2, -2, 1)$ and $\vec{b} = (1, -2, 2)$.The formula for the cosine of the angle $	heta$ be

Vedclass · Accepted Answer

$\cos^{-1}\left(\frac{8}{9}\right)$

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(B) Let the direction ratios of the two lines be $\vec{a} = (2, -2, 1)$ and $\vec{b} = (1, -2, 2)$.The formula for the cosine of the angle $	heta$ between two lines with direction ratios $(a_1, b_1, c_1)$ and $(a_2, b_2, c_2)$ is given by:$\cos 	heta = \frac{|a_1 a_2 + b_1 b_2 + c_1 c_2|}{\sqrt{a_1^2 + b_1^2 + c_1^2} \sqrt{a_2^2 + b_2^2 + c_2^2}}$Substituting the given values:$\cos 	heta = \frac{|(2)(1) + (-2)(-2) + (1)(2)|}{\sqrt{2^2 + (-2)^2 + 1^2} \sqrt{1^2 + (-2)^2 + 2^2}}$Calculating the numerator:$|2 + 4 + 2| = 8$Calculating the denominators:$\sqrt{4 + 4 + 1} = \sqrt{9} = 3$$\sqrt{1 + 4 + 4} = \sqrt{9} = 3$Thus,$\cos 	heta = \frac{8}{3 	imes 3} = \frac{8}{9}$.Therefore,$	heta = \cos^{-1}\left(\frac{8}{9}ight)$.

The angle between the lines with direction ratios $(2, -2, 1)$ and $(1, -2, 2)$ is

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