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?