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

Let $\frac{x-3}{2}=\frac{y-2}{3}=\frac{z-1}{\lambda }=t\Rightarrow x=2t+3,y=3t+2,z=\lambda t+1.(x,y,z)$ lies on $\frac{x-2}{3}=\frac{y-3}{2}=\frac{z-2}{3}$ $\Rightarrow \frac{2t+1}{3}=\frac{3t-1}{2}=\frac{\lambda t-1}{3}\Rightarrow t=1\Rightarrow$ point of intersection is (5, 5, 5), and $3(5)+5+5=25$.