Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

From given data, we write $\mathrm{A}\equiv (0,\mathrm{b},\mathrm{c})$ and $\mathrm{B}\equiv (\mathrm{a},0,\mathrm{c})$ Equation of plane passing through $\mathrm{A},\mathrm{B}$ and $\mathrm{O}$ is $$\begin{array}{rl}& \left|\begin{array}{lll}x-0& y-0& z-0\\ 0-0& b-0& c-0\\ a-0& 0-0& c-0\end{array}\right|=0\Rightarrow \left|\begin{array}{lll}x& y& z\\ 0& b& c\\ a& 0& c\end{array}\right|=0\\ & \therefore x(bc)-y(-ac)+z(-ab)=0\Rightarrow bcx+acy-abz=0\end{array}$$ Dividing both sides by abc, we get $\frac{\mathrm{x}}{\mathrm{a}}+\frac{\mathrm{y}}{\mathrm{b}}-\frac{\mathrm{z}}{\mathrm{c}}=0$