OpenVR: Obtaining direction vector from Pose transformation matrix

I'm trying to find the direction in which my oculus touch controller is pointing at any given point in time in OpenVR. (The direction in which you would render a ray pointer from the controller) I am using the following function

GetControllerStateWithPose( TrackingUniverseStanding, deviceId, &controllerState, sizeof(controllerState), &trackedDevicePose);

In the picture below, I understand that the position is described by m12 m13 and M14 for x, y and z. But how do I use the m0 to m10 values to find a direction vector in which the controller points at any given time.

Can't post images because of my new account but it can be found here

Would I simply multiply this matrix by [1,1,1,0]^T? Or maybe [0,0,1,0]^T since Z axis is the describes as the forward direction