Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Equation of plane passing through the point $(2,3,1)$ is $a(x-2)+b(y-3)+c(z-1)=0$ $\dots (1)$ Given point $(4,-5,3)$ lies on plane $2a-8b+2c=0$ $\dots (2)$ Since plane is parallel to $\mathrm{Y}$-axis, having d.r. $(0,1,0)$ (a) $(0)+(\mathrm{b})(1)+(\mathrm{c})(0)=0\Rightarrow \mathrm{b}=0$ Putting in equation (2) we get $2a+2c=0\Rightarrow a=-c$ Putting values of $\mathrm{a},\mathrm{b}$ in equation (1) $\begin{array}{rl}& -c(x-2)+c(z-1)=0\\ \therefore & (x-2)-(z-1)=0\\ \therefore & x-z=1\end{array}$