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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