By Kardi Teknomo, PhD .
LinearAlgebra

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Vector Triple Dot Product

Vector triple dot product Triple Dot Product is a multiplication of three vectors that produce another vector. First vector Triple dot product and vector Triple dot product are multiplied using inner product , and then the scalar result of the inner product is used as a scalar multiple to the vector Triple dot product . Geometrically triple dot product is the same as vector scalar multiple that stretch or shrink the vector Triple dot product based on the angle between vector Triple dot product and vector Triple dot product . When the vector Triple dot product and vector Triple dot product are collinear the angle is zero and the triple dot product exactly the same as vector Triple dot product . As the angle between vector Triple dot product and vector Triple dot product is larger than zero, the length of vector Triple dot product reduces up to zero-vector when the angle between vector Triple dot product and vector Triple dot product is perpendicular.

Example
Suppose we have three vectors Triple dot product , Triple dot product and Triple dot product .


First we compute dot product
Triple dot product
Then, the triple dot product is just scalar multiple of the first vector
Triple Dot Product

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

a ( b . c )

Properties

Some important properties of related to triple dot product is

  • Vector triple dot product is related to triple cross product:
    • Triple dot product
    • Triple dot product

See Also : Scalar triple product , triple cross product

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