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Applications of the Dot Product and Cross Product When a force is acting on an object so that the object is moved from one point to another, we say that the force has Eg.1: A rickshaw driver pulls his cart at an angle of 30 with the horizontal. If his current customer requires him to pull up on the rickshaw handles with a force of 60 N, and the trip is a total of 750 m, how much work, in J, has the rickshaw driver done over the course of this trip? The cross product of two vectors, defined by a and b can be used to find the area of a parallelogram. N.B. A triangle is half of a parallelogram along the diagonals.Eg.2: Determine the area ofQRSwith verticesQ(2 ,4, ] ),R{3,-3 , 5)and S (-2,0,2). The cross product can also be used in the consideration of forces that involve rotation, or turning abOut a point or an axis. The rotational or turning effect ofa force is called . E: is the force applied to the lever (or wrench). 4 is the distance from the pivot point to the point where the force has been applied. Its A tail is at the pivot point and its head at the point where :5- is applied. 6' is the angle between and :0 " The unit for torque is the Eg.3: A force of'30 N is used to open a hinged lid on the top ofa box. The force is applied 30 cm from the hinge at an angle of 45\". Calculate the magnitude of the torque