If the coordinates of the points A, B, C, D a | vedclass

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(D) The direction ratios of line $AB$ are $(4-1, 5-2, 7-3) = (3, 3, 4)$.The direction ratios of line $CD$ are $(2-(-4), 9-3, 2-(-6)) = (6, 6, 8)$.Let

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(D) The direction ratios of line $AB$ are $(4-1, 5-2, 7-3) = (3, 3, 4)$.The direction ratios of line $CD$ are $(2-(-4), 9-3, 2-(-6)) = (6, 6, 8)$.Let the angle between the lines be $	heta$. The formula for the angle between two lines with direction ratios $(a_1, b_1, c_1)$ and $(a_2, b_2, c_2)$ is $\cos 	heta = \frac{|a_1 a_2 + b_1 b_2 + c_1 c_2|}{\sqrt{a_1^2 + b_1^2 + c_1^2} \sqrt{a_2^2 + b_2^2 + c_2^2}}$.Here,$a_1=3, b_1=3, c_1=4$ and $a_2=6, b_2=6, c_2=8$.Note that $(a_2, b_2, c_2) = 2(a_1, b_1, c_1)$,which means the lines are parallel.Therefore,$\cos 	heta = \frac{|(3)(6) + (3)(6) + (4)(8)|}{\sqrt{3^2+3^2+4^2} \sqrt{6^2+6^2+8^2}} = \frac{|18+18+32|}{\sqrt{34} \sqrt{136}} = \frac{68}{\sqrt{34} \cdot 2\sqrt{34}} = \frac{68}{2 \cdot 34} = 1$.Since $\cos 	heta = 1$,the angle $	heta = 0^\circ$ or $0$ radians.Since $0$ is not among the options $A, B, C$,the correct answer is $D$.

If the coordinates of the points $A, B, C, D$ are $(1, 2, 3), (4, 5, 7), (-4, 3, -6)$ and $(2, 9, 2)$ respectively,then the angle between the lines $AB$ and $CD$ is

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