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.