A force F of 6 units acts in the direction 30 degrees west of north. An object is constrained to move north-westerly, that is, 45 degrees west of north. (a) Sketch the force vector roughly to scale on a set of axes that has the positive y axis pointing north, and write F using exact values, either in the form (x; y) or else in the form xi + yj. (b) Write a vector in the direction of the given movement of the object. (c) Without using trigonometric functions, ¯find both the scalar component and the vector projection of F in the direction of movement of the object. Write both answers as exact values, not decimal approximations.