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DotProduct

DotProduct[v1,v2]

gives the dot product of the two 3-vectors v1, v2 in the default coordinate system.

DotProduct[v1,v2,coordsys]

gives the dot product of v1 and v2 in the coordinate system coordsys.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
See Also
Tech Notes
Related Guides
VectorAnalysis`
VectorAnalysis`

DotProduct

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

DotProduct[v1,v2]

gives the dot product of the two 3-vectors v1, v2 in the default coordinate system.

DotProduct[v1,v2,coordsys]

gives the dot product of v1 and v2 in the coordinate system coordsys.

Details and Options

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

Examples

Basic Examples  (3)

Wolfram Language code: Needs["VectorAnalysis`"]

Dot product of two Cartesian vectors:

Wolfram Language code: a = {1, 2, 5};
Wolfram Language code: b = {2, 3, -7};
Wolfram Language code: DotProduct[a, b]
Wolfram Language code: Needs["VectorAnalysis`"]

Verify that a pair of vectors are orthogonal:

Wolfram Language code: a = {1, 3, -1};
Wolfram Language code: b = {2, 5, 17};
Wolfram Language code: DotProduct[a, b]
Wolfram Language code: Needs["VectorAnalysis`"]

Dot product of vectors in cylindrical coordinates:

Wolfram Language code: a = {1 / 3, 1 / 2, 7};
Wolfram Language code: b = {1 / 2, 1 / 5, 1};
Wolfram Language code: DotProduct[a, b, Cylindrical]//Simplify

Compare with the result from conversion to Cartesian coordinates:

Wolfram Language code: DotProduct[CoordinatesToCartesian[a, Cylindrical], CoordinatesToCartesian[b, Cylindrical]]//Simplify