By Kardi Teknomo, PhD.
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Triple cross product is also called vector triple product. It is a multiplication of three vectors that produces a vector
**Example**
Suppose we have three vectors , and.
First we compute cross product
Then, the triple cross product is
Geometrically, vector triple product is perpendicular to and lies in the plane span by and .
The interactive program below helps you to compute triple cross product algebraically. You input 3 vectors of the same dimension. The program output is the vector triple product. Random example button will generate random vectors at the right format.
## Properties
Some important properties of related to triple cross product are
- Vector triple product is zero when any of the two vectors are collinear. Collinear means they lie on the same line or parallel lines.
- Vector triple product for non-collinear vectors has unique linear combination expansion in the form of where and . Thus,
- Similarly,
- Summation of triple cross product in a cycle is zero. This property is called Jacobi identity
**See also**: Triple dot product, cross product, inner product, scalar triple product
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**Preferable reference for this tutorial is**
Teknomo, Kardi (2011) Linear Algebra tutorial. http:\\people.revoledu.com\kardi\
tutorial\LinearAlgebra\ |