ScalarTripleProduct

As of Version 9.0, vector analysis functionality is built into the Wolfram Language »

ScalarTripleProduct[v₁,v₂,v₃]

gives the scalar triple product of the three 3-vectors v₁, v₂, and v₃ in the default coordinate system.

ScalarTripleProduct[v₁,v₂,v₃,coordsys]

gives the scalar triple product of v₁, v₂, and v₃ in the coordinate system coordsys.

Details and Options

To use ScalarTripleProduct, you first need to load the Vector Analysis Package using Needs["VectorAnalysis`"].
ScalarTripleProduct[v₁,v₂,v₃,coordsys] is computed by converting v₁, v₂, and v₃ to Cartesian coordinates and then forming the scalar triple product.

Wolfram Language code: Needs["VectorAnalysis`"]

Compute the scalar triple product of three vectors in space:

Wolfram Language code: r1 = {1, -3, 2};

Wolfram Language code: r2 = {3, 7, -5};

Wolfram Language code: r3 = {4, 1, 6};

Wolfram Language code: ScalarTripleProduct[r1, r2, r3]

Use Det to obtain the same answer:

Wolfram Language code: Det[{r1, r2, r3}]

Find the equation of the plane passing through the points with position vectors r1, r2, and r3:

Wolfram Language code: r = {x, y, z};

Wolfram Language code: ScalarTripleProduct[r - r1, r2 - r1, r3 - r1] == 0

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