Are "direction of force" and "plane of application" valid concepts in mechanical physics, or are these terms I've made up? Just from the terms alone I'd assume that plane of application is perpendicular to direction of force. But I wonder if that's always the case.
… force is a vector … Hi Dave! "direction of force" is certainly essential in mechanical physics - Newton's second law (which is about as fundamental as you can get!) says applied force = (rate of change of) momentum, and momentum certainly has a direction. The direction is as much an essential part of any force as it is of any velocity, or of any momentum or acceleration! In mathematical terms, force is a vector (and so, like velocity, momentum, or acceleration, obeys the vector "law of addition"). "plane of application" …? … I haven't come across.
Sounds about right to me. You can use whatever definition you want as long as you state what you mean by it.
If you want to be super picky about it, forces have a magnitude and a direction. They are distributed on a differential area normally and tangentially. As the differential area collapses the differential force acts on a point. A plane of application would imply a stress, not a force.