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When you wish to charge reference frames. For instance you may want to change from the natural reference frame for an aircraft (x along the aircraft axis, y in the plane of the floor to the right, and z in the direction of the cabin roof) to an Earth base axis system.Why would we want to transform a vector in our normal basis (xyz axes) to another basis? The only situation I can recall is when we are looking at a force applied on an inclined plane. Are there any other real life examples where this may be necessary?