Cross Product Methods

Cross Product Methods - Cross Products in Action - An...

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Cross Products in Action - An Example Involving 3x3 Determinants Question: Compute the cross product, u × v , of the following two vectors: u = < 3, 1, 0 >, v = < 5, 2, 1> Solution: But computing the value of what is called the ”determinant of a matrix”, can be tricky. We'll leave the theory for another course, but for a 3x3 matrix, there there are two common methods: _________________________________________ Method #1: Using the Diagonals Copy the first two columns to the right of the matrix. Compute the product along the diagonal, down to the right, and add. Compute the products along the diagonal, down and to the left, and subtract. _________________________________________ Page # 1 of 3 3, 1, 0 5, 2, 1 3 1 0 5 2 1   i j k uv 3 1 0 3 1 (1)( 1) (0)(5) (3)2 (1)5 (0)(2) (3)( 1) 5 2 1 5 2 ( 1 0) (0 3) (6 5) < 1, 3, 1      ijk i j ij k k i j
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Method #2: Using Minors Write each of the 2x2 minors corresponding to i , j and k . Compute the value of each minor. (call them M 11 , M 12 , M 13 respectively.) Compute M 11 i M 12 j + M 13 k But what's a minor?
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Cross Product Methods - Cross Products in Action - An...

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