Consider a particle P of mass m moving freely in a Euclidean plane under the influence of a constant force F. Introduce oblique Cartesian coordinates q, q (x) = ( 9() x, x being rectangular Cartesian. (a) Calculate the covariant basis vectors a (i = 1,2) and the metric coefficients aap (a, = 1,2). (b) Write the position and velocity vectors of P using the covariant basis. (c) Apply Lagrange's equations in the form d at (300) - 30 = Q = Faa, (a = 1,2). dt qa