Vectors Question

To control the roll of an airplane (rotation about the x-axis in the figure below), the ailerons are normally actioned in opposite directions on each wing. Engineers in charge of dimensioning the wing are assessing what would happen if one of ailerons was malfunctioning. They estimate that the airplane would still be controllable if the effective rotation axis would deviate by less than 30° compared to the x-axis.

(a) Calculate the moment of force M (as a vector) about the centre of mass G = (0, 0, 0) due
to a left aileron force F =(0,0,F)applied at the point A = (-3, 4, 0.5) (in metres);
(b) Given that rotations occur about the centre of mass, find the direction of the axis of rotation induced by the aileron force F as a (normalised) 3D unit vector;
(c) Is the airplane controllable in this situation according to the engineers' criterion?

Post Merge: A month ago

Question with diagram