What direction does the torque vector have if a force is applied to an object?

The direction of the torque vector depends on both the direction of the applied force and the position at which that force is applied in relation to the pivot point of the object. Torque is calculated as the cross product of the position vector (from the pivot point to the point where the force is applied) and the force vector.

When you apply a force to an object, for example, if the force is directed in a way that tends to cause a counterclockwise rotation around a pivot, the resulting torque vector will be oriented perpendicular to the plane formed by the position vector and the force vector. In many standard conventions, if the torque direction is determined to create a counterclockwise motion, it will typically point out of the screen towards you. Conversely, if the force causes a clockwise rotation, the torque vector will point into the screen.

Thus, what influences the torque vector's direction is specifically how and where the force is applied relative to the object's pivot point, establishing a three-dimensional relationship between rotation, position, and force. In this case, stating that the torque vector is directed into the screen indicates that the force applied tends to create a clockwise rotation about the pivot point.