the cross product is a measure of how perpendicular two vectors are si
. The cross product is a measure of how perpendicular two vectors are, since its magnitude islargest when they are perpendicular. What is more, the result of the cross product is a vectorwhich 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 crossproduct is mathematically indicated as A × B. The magnitude of A × B is given by theformula AB sin 0. The final result is this value times a unit vector perpendicular to the planecontaining A and B. However, this still leaves two possible unit vector directions! Since ourculture has chosen to use coordinate systems which are "right-handed," the arithmetic is easierif we also choose a right-handed method to choose one of the two possible unit vectors. Thismethod is called the "Right Hand Rule" a)Assume we want to evaluate C = A × B. Using the righthand rule that we learned last semester, which vector is inthe direction of: Your straight RH fingers: Your curled RH fingers (or palm): Your RH thumb:
OGiven vectors A and B shown above, what is the direction of vector C = A × B? What is the direction of the cross product B x A? Is it the same as your answer to partb)? d) Now sketch A and B in two orientations, one that gives the maximum magnitude ofJA x B| = AB, and one that gives the minimum magnitude of |A x B| = 0.
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