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MAT 240 Calculus III Vector Handout – Cross Product Applications 1. Do the following: A) Recall the formula to find the area of a parallelogram. B) Consider the two vectors u = 3, 4 , v = 7, 0 , sketch the parallelogram formed by these two vectors and then use the formula from part A) to find that area of this parallelogram. C) Find u v D) What conclusion can you make from this exercise? 2. Given the vectors v = 2, 1, 2 and w = 1, 2, 3 find the following: A) Find v x w B) Area of the parallelogram made by v and w. C) Show that v x w is perpendicular to v and w 3. A bike pedal is pushed with a force of 60 Newton. The shaft of the pedal is 0.2 meters long. Find the torque about the point P. 4. A force of 200 N is applied at an angle of 18° to a point near the end of a monkey wrench. Find the torque generated by this force about the center of the bolt. 5. Find that angle between the two vectors u = 5, 12 , v = 3, 4 by doing the following: A) Use the dot product and cosine formula. B) Use the cross product and sine formula. C) Conclusions?