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If the coordinates of the points A, B, C, D be $(1,2,3),(4,5,7)$, $(-4,3,-6)$ and $(2,9,2)$ respectively, then find the angle betwen the lines $\mathbf{A B}$ and $\mathrm{CD}$.
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Direction ratios of $\mathrm{AB}$ when $\mathrm{A}$ and $\mathrm{B}$ are $(1,2,3),(4,5,7)$ are $4-1,5-2,7-3$ or $3,3,4$ Direction ratios of the line joining the points $\mathrm{C}(-4,3,-6)$ and $\mathrm{D}(2,9,2)$ are $2+4,9-3,2+6$ or $6,6,8$
Derection ratio of $A B$ and $C D$ are proportional
$\Rightarrow$ Angle between these lines is zero.
$\Rightarrow$ The lines $\mathrm{AB}$ and $\mathrm{CD}$ are parallel.
Derection ratio of $A B$ and $C D$ are proportional
$\Rightarrow$ Angle between these lines is zero.
$\Rightarrow$ The lines $\mathrm{AB}$ and $\mathrm{CD}$ are parallel.
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