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

Let the equation of a plane containing the line be $l(\mathrm{x}-1)+\mathrm{m}(\mathrm{y}+2)+\mathrm{nz}=0$. Then $2l-3\mathrm{m}+5\mathrm{n}=0$ and $l-\mathrm{m}+\mathrm{n}=0$.

$$\begin{array}{ll}\therefore & \frac{l}{2}=\frac{\mathrm{m}}{3}=\frac{\mathrm{n}}{1}\\ \therefore & \text{ the plane is }2(\mathrm{x}-1)+3(\mathrm{y}+2)+\mathrm{z}=0\\ \text{ i.e. }& 2\mathrm{x}+3\mathrm{y}+\mathrm{z}+6=0\\ \therefore & \mathrm{a}=2,\mathrm{b}=-3,\mathrm{c}=1\\ \therefore & 10^3\mathrm{a}+10^2\mathrm{b}+10\mathrm{c}=2000-300+10=1710\text{ Ans. }\end{array}$$