Question

# 2. The cross product is a measure of how perpendicular two vectors are, since its magnitude is largest when they are perpendicular. What is more, the result of the cross product is a vector which is perpendicular (normal) to the plane containing the two vectors being multiplied.Hence, it is sometimes called the vector product. For the two vectors A and B, the cross product is mathematically indicated as A x B. The magnitude of A x B is given by the formula AB sin . The final result is this value times a unit vector perpendicular to the plane containing A and B. However, this still leaves two possible unit vector directions! We use the"Right Hand Rule" to determine the direction of the result. If you don't remember how to do this, ask one of your instructors. (a) Using arrows, sketch two vectors A and B in some orientation with a finite angle 0 between them. Choose an angle between 0° and 180°, but not 90°, and label the arrows. (b) Assuming the two vectors lie in the plane of your paper, what is the direction of the result of the cross product A x B? (c) What is the direction of the cross product B × A? Is it the same as your answer to part b)? (d) Now sketch new vectors C and D in two different relative orientations, one that gives the maximum magnitude of |C x D| = CD, and one that gives the minimum magnitude of|C x D| = 0.  Fig: 1  Fig: 2  Fig: 3  Fig: 4  Fig: 5