ch12s4 - 12.4 The Cross Product The cross product is a...

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12.4 The Cross Product The cross product is a vector, sometimes called the vector product. Cross products are only found with 3-dimensional vectors. Cross Product 1, 2 3 1 2 3 23 32 31 13 12 21 ,, , aa a b b b ab ab ab == ×= Determinants can be used to find this product. The TI-85 and TI-86 will also perform this operation. Determinants and Cross Product 123 ad bc cd aaa bbb aa bb =− + i j k ijk Example: Find the cross product for 1 , 2 ,3 5 ,1 ,2 =− = . Theorems, etc. (a) The cross product is orthogonal to both a and b. (b) If θ is the angle between a and b then sin θ . (c) Two nonzero vectors a and b are parallel if and only if the cross product is 0.
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(d) The length of the cross product is equal to the area of the parallelogram determined by a and b . Example: Find a vector orthogonal to the plane through the points
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This note was uploaded on 01/20/2012 for the course MATH 2057 taught by Professor Estrada during the Fall '08 term at LSU.

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ch12s4 - 12.4 The Cross Product The cross product is a...

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