MATH 101 Lecture Notes - Lecture 2: Triple Product, Laplace Expansion, Cross Product
5 Sep 2016
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Math 212 section 11. 4 the cross product of two vectors in space. Learning objective: the learner will be able to (1) find the cross product of two vectors in space; (2) use the triple scalar product of three vectors in space; (3) use the cross product to solve torque application problems. Many applications in physics, engineering, and geometry involve finding a vector in space that is orthogonal to two given vectors. You will study a product that will yield such a vector. It is called the cross product, and it is most conveniently defined and calculated using the standard unit vector form. Because the cross product yields a vector, it is also called the vector product. A convenient way to calculate (cid:1873) (cid:1874) is to use the following determinant form with cofactor expansion. Note the minus sign in front of the (cid:2836) -component. Each of the three 2 2 determinants can be evaluated by using the following diagonal pattern.
