Find the acute angle between two lines with d | vedclass

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(B) Let the direction ratios of the two lines be $(a_1, b_1, c_1) = (2, 3, 6)$ and $(a_2, b_2, c_2) = (1, 2, 2)$.The formula for the angle $	heta$ be

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$\cos ^{ - 1} \left( \frac{20}{21} \right)$

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(B) Let the direction ratios of the two lines be $(a_1, b_1, c_1) = (2, 3, 6)$ and $(a_2, b_2, c_2) = (1, 2, 2)$.The formula for 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:$\cos 	heta = \left| \frac{a_1 a_2 + b_1 b_2 + c_1 c_2}{\sqrt{a_1^2 + b_1^2 + c_1^2} \sqrt{a_2^2 + b_2^2 + c_2^2}} ight|$Substituting the values:$\cos 	heta = \left| \frac{(2)(1) + (3)(2) + (6)(2)}{\sqrt{2^2 + 3^2 + 6^2} \sqrt{1^2 + 2^2 + 2^2}} ight|$Calculating the numerator:$2 + 6 + 12 = 20$Calculating the denominators:$\sqrt{4 + 9 + 36} = \sqrt{49} = 7$$\sqrt{1 + 4 + 4} = \sqrt{9} = 3$Thus,$\cos 	heta = \left| \frac{20}{7 	imes 3} ight| = \frac{20}{21}$.Therefore,$	heta = \cos ^{ - 1} \left( \frac{20}{21} ight)$.

Find the acute angle between two lines with direction ratios $2, 3, 6$ and $1, 2, 2$ respectively.

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