## Vector Triple Cross Product

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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