Student[VectorCalculus]
DotProduct
compute the dot product of Vectors and differential operators
Calling Sequence
Parameters
Description
Examples
DotProduct(v1, v2)
v1 . v2
v1
-
Vector or differential operator
v2
The DotProduct(v1, v2) calling sequence computes the dot product (scalar product) of v1 and v2, where v1 and v2 can be Vectors, vector fields, Student[VectorCalculus]:-Del, or Student[VectorCalculus]:-Nabla.
The Student[VectorCalculus] package has a `.` operator that you can use in place of the DotProduct command. For example, DotProduct(v1, v2) is equivalent to v1·v2.
Also, Del·F is equivalent to Divergence(F).
withStudentVectorCalculus:
DotProducta,b,c,d
ac+bd
SetCoordinatespolarr,θ
polarr,θ
v≔RootedVectorroot=1,2,a,b
v≔ab
w≔RootedVectorroot=1,2,c,d
w≔cd
v·w
F≔VectorFieldr2,θ
Del·F
3r2+1r
DivergenceF
SetCoordinatescartesianx,y,z
cartesianx,y,z
L≔VectorFieldx,y,z·Delfx,y,z
L≔x∂∂xfx,y,z+y∂∂yfx,y,z+z∂∂zfx,y,z
See Also
combine
Student[VectorCalculus][Del]
Student[VectorCalculus][Divergence]
Student[VectorCalculus][Laplacian]
Student[VectorCalculus][Nabla]
Student[VectorCalculus][SetCoordinates]
Student[VectorCalculus][Vector]
Student[VectorCalculus][VectorField]
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