Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

d.r's of perpendicular to both the given lines can be obtained by $\begin{array}{rl}& \frac{a}{2\times 5-2\times 3}=\frac{b}{-3\times 3-1\times 5}=\frac{c}{1\times 2-(-3)\times 2}\\ & \Rightarrow \frac{a}{4}=\frac{b}{-14}=\frac{c}{8}\\ & \Rightarrow \text{ d.r’s are }<2,-7,4>\end{array}$ now, required equation of the line $\frac{x-2}{2}=\frac{y-1}{-7}=\frac{z-3}{4}$ $\Rightarrow \frac{x-2}{2}=\frac{1-y}{7}=\frac{z-3}{4}$