Drag and rotate a THREE.Plane


I come here a lot but this is the first time I post, sorry in advance for everything I will do wrong.

I want the user to control a clipping plane by using a cube which he can drag and rotate with transformControls, this cube being a representation of the clipping plane.
THREE.Plane not being an object, I could copy the rotation of the cube to the plane using .applyQuaternion on the normal of the clipping plane.
But I struggle trying to translate this plane. My little matrix knowledge is not that fresh anymore, which operation should I use to achieve my goal?