MATH 215 Chapter Notes - Chapter 12.4: Triple Product, Cross Product, Parallelepiped
Document Summary
De nition: if a = and b = , then the cross product of a and b is the vector a x b = . The cross product, unlike the dot product, is a vector. We constructed the cross product of a x b so that it would be perpendicular to both a and b. This is one of the most important properties of a cross product. Theorem: the vector a x b is orthogonal (perpendicular) to both a and b. Since (a x b) b = 0, therefore a x b is orthogonal to both a and b. Theorem: if is the angle between a and b (so 0 <= <= pi), then: | a x b | = |a||b|sin . Corollary: two nonzero vectors a and b are parallel if and only if a x b = 0.
