By Kardi Teknomo, PhD .
LinearAlgebra

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Scalar triple product is a multiplication of three vectors that produces a scalar Scalar Triple Product

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

First we compute cross product
Scalar Triple Product

Then, the scalar triple product is
Scalar Triple Product

Geometrically, scalar triple product is equal to the volume of parallelepiped. The based area of the parallelepiped is a parallelogram whose area is equal to the absolute value of the cross product Scalar Triple Product .


Scalar Triple Product

The interactive program below helps you to compute Scalar triple product algebraically. You input 3 vectors of the same dimension. The program output is the scalar triple product. Random example button will generate random vectors at the right format.

(a * b ) . c

Properties

Some important properties of related to scalar triple product are

  • Scalar triple product is invariant under cyclic permutation of the vectors, that is Scalar Triple Product
  • Scalar triple product is zero if two of the vectors lie on the same plane or are parallel to the same plane (i.e. coplanar) Scalar Triple Product .
  • Three vectors are linearly dependent (coplanar) if and only if their scalar triple product is zero Scalar Triple Product .
  • Three vectors form a basis if and only if their scalar triple product is not zero Scalar Triple Product . The basis is right handed if the scalar triple product is positive Scalar Triple Product and called left handed if the scalar triple product is negative Scalar Triple Product .

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

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