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K^3/Cross product/Properties/Fact

From Wikiversity

The cross product on fulfills the following properties (where and ).

  1. We have
  2. We have

    and

  3. We have

    if and only if and are linearly dependent.

  4. We have
  5. We have

    where denotes the formal evaluation in the sense of the standard inner product.

  6. We have

    where denotes the formal evaluation in the sense of the standard inner product.