By Kardi Teknomo, PhD .
LinearAlgebra

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Triple cross product is also called vector triple product. It is a multiplication of three vectors that produces a vector Triple Cross Product

Example
Suppose we have three vectors Triple Cross Product , Triple Cross Product and Triple Cross Product .


First we compute cross product
Triple Cross Product


Then, the triple cross product is
Triple Cross Product

Geometrically, vector triple product is perpendicular to Triple Cross Product and lies in the plane span by Triple Cross Product and Triple Cross Product .
Triple Cross Product

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.

a * b * c

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 Triple Cross Product for non-collinear vectors has unique linear combination expansion in the form of Triple Cross Product where Triple Cross Product and Triple Cross Product . Thus, Triple Cross Product
  • Similarly, Triple Cross Product
  • Summation of triple cross product in a cycle is zero Triple Cross Product . This property is called Jacobi identity

See also : Triple dot product , cross product , inner product , scalar triple product

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