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Triple Cross Product

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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.

vector a vector b vector c x x

## 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