School of Mathematics and Statistics, The University of Sydney
 11. The vector product
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Vector products and the area of a triangle

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The magnitude of the product u × v is by definition the area of the parallelogram spanned by u and v when placed tail-to-tail. Hence we can use the vector product to compute the area of a triangle formed by three points A, B and C in space.

                        C          - -->          AC  A          --->        AB                    B

It follows that the area of the triangle is

     1---->    ---> A =  2|AB  × AC  |.

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