Question: Find the equation of the plane containing two lines (x-1)/2=(y-2)/3=(z-3)/4 and (x-2)/3=(y-3)/4=(z-4)/5 . Solution : First we shall find direction vector of the lines \[\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\] and \[\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}\] are \[\vec{d_1}=2\hat{i}+3\hat{j}+4\hat{k},\ \vec{d_2}=3\hat{i}+4\hat{j}+5\hat{k}\] Respectively. Therefore direction vector of the perpendicular line to…
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