Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Let $\frac{x-3}{1}=\frac{y+1}{3}=\frac{z-6}{-1}=\lambda$ $\Rightarrow x=3+\lambda ,y=3\lambda -1,\mathrm{z}=-\lambda +6$ Let $\frac{x+5}{7}=\frac{y-2}{-6}=\frac{z-3}{4}=\mu$ $\Rightarrow x=7\mu -5,y=-6\mu +2,\mathrm{z}=4\mu +3$ Both the given lines intersect each other. $\begin{array}{rl}& \text{ So, }\lambda +3=7\mu -5\\ & \Rightarrow 7\mu -\lambda =\mathrm{8...}(i)\end{array}$ Also, $3\lambda -1=-6\mu +2$ $\Rightarrow 6\mu +3\lambda =3$...(ii) From (i) and (ii), we get $\begin{array}{rl}& \mu =1,\lambda =-1\\ & \text{ i.e., }x=2,y=-4,\mathrm{z}=7\end{array}$ $\therefore$ Co-ordinates of the intersection of the given lines are $\mathrm{R}(2,-4,7)$ Hence, reflection of $\mathrm{R}$ in the $xy$-plane is $(2,-4,-7)$.