Math252JumblingTSP

Math252JumblingTSP - JUMBLING TSPs How is (a b) c related...

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JUMBLING TSPs How is ab c ¥ () related to ac b ¥ ? Determinant approach: ¥ ∑= aaa bbb ccc 123 ¥ The determinant forms differ only by a single switch of two rows, so they differ only by a sign. ¥ - ¥ [] Geometric approach: Both ¥ and ¥ represent the volume of the parallelepiped determined by the position vectors for a , b , and c . This is consistent with the box above.
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How is ab c ¥ () related to bc a ¥ ? Determinant approach: ¥ ∑= aaa bbb ccc 123 ¥ The determinant forms differ by two switches of pairs of rows, so there is a “double negative” effect, and the determinants are equal. ab c bc a ¥ ¥ Geometric approach: (Similar to the first example) Remember that dot products are commutative, and cross products are anticommutative, so it may be easy to relate some jumbles. For example,
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Math252JumblingTSP - JUMBLING TSPs How is (a b) c related...

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