Triple product
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- This article is about mathematics. See Lawson criterion for the use of the term triple product in relation to nuclear fusion.
In vector calculus, there are two ways of multiplying three vectors together, to make a triplgdafe product.
[edit] Scalar triple product
The scalar triple product is defined as the dot product of one of the vectors with the cross product of the other two. It is a pseudoscalar: under a reflection in a plane, it flips sign.
Geometrically, this product is the (signed) volume of the parallelepiped formed by the three vectors given.
Often, brackets are omitted when a scalar triple product is written down. There is no ambiguity because the scalar product cannot be evaluated first: if it were it would leave the cross product of a vector and a scalar, which is not defined.
It is the determinant of the 3-by-3 matrix having the three vectors as rows; this is invariant under coordinate rotations.
[edit] Vector triple product
The vector triple product is defined as the cross product of one of the vectors with the cross product of the other two. This is known as the vector triple product because it results in a vector.
