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

Equation of line joining the points (1,1,1) and (0,0,0) is $$\begin{array}{rl}\frac{x-0}{1-0}& =\frac{y-0}{1-0}=\frac{z-0}{1-0}=\lambda \\ \Rightarrow & x=y=z=\lambda \end{array}$$ So, the point is $(\lambda ,\lambda ,\lambda )$ The point intersects the plane $2x+2y+z=10$ $\therefore 2(\lambda )+2(\lambda )+\lambda =10$ $\Rightarrow 5\lambda =10$ $\Rightarrow \lambda =2$ Hence, the point is (2,2,2) .