12.4 The Cross ProductThe cross product is a vector,sometimes called the vector product.Cross products are only found with 3-dimensional vectors. Cross Product 1,23123233231131221,,,,,a aab bba ba ba ba ba ba b==×=−−−ababDeterminants can be used to find this product. The TI-85 and TI-86 will also perform this operation. Determinants and Cross Product 123123231312231312123123,,,,abadbccdaaab bbaaaaaabbbbbbaaabbb=−==×=−+×=ababijkijkabExample: Find the cross product for 1,2,35,1,2=−=−−ab. Theorems, etc. (a) The cross product is orthogonal to both aand b. (b) If θis the angle between aand b then sinθ×=abab. (c) Two nonzero vectors aand b are parallel if and only if the cross product is 0.
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