Two forces, F1=[200,500,450] and F2=[200,400,300], both measured in newtons, act on an object through a displacement defined by d=[4,2,13], measured in meters.

(a) Use the concept of vector projection to determine the total magnitude of the force applied on the object in the direction of its displacement, to the nearest newton.

(b) Using the dot product, find the total work done on the object to the nearest joule.

(c) Given the gravity is a force in the direction of the negative z-axis, determine the total work done against gravity to the nearest joule.