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

Given line is $\frac{x-1}{2}=\frac{y-2}{-3}=\frac{z+5}{4}$ Let $\frac{x-1}{2}=\frac{y-2}{-3}=\frac{z+5}{4}=\lambda$ $\begin{array}{ll}\therefore & x-1=2\lambda ,y-2=-3\lambda ,\mathrm{z}+5=4\lambda \\ & x=2\lambda +1,y=-3\lambda +2,\mathrm{z}=4\lambda -5\\ \therefore & 2x+4y-\mathrm{z}=3\\ & \Rightarrow 2(2\lambda +1)+4(-3\lambda +2)-(4\lambda -5)=3\\ & \Rightarrow 4\lambda +2-12\lambda +8-4\lambda +5=3\\ & \Rightarrow -12\lambda =3-15\\ & \Rightarrow \lambda =1\\ \therefore & x=3,y=-1,\mathrm{z}=-1,\end{array}$ $\therefore$ Required co-ordinates are: $(3,-1,-1)$