Intersection of planes

Question

A line perpendicular to the plane $ 3x-5y+4z-11=0 $ passes through the origin. At what point does this normal intersects the plane?

Answer 1

The equations of the line are

$$x=3t$$ $$y=-5t$$ $$z=4t$$ thus for the intersection we have

$$9t+25t+16t=11$$

so $$x=\frac{3}{25}$$ $$y=-\frac{1}{5}$$ $$z=\frac{4}{25}$$