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Student[VectorCalculus][DotProduct] - compute the dot product of Vectors and differential operators
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Calling Sequence
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DotProduct(v1, v2)
v1 . v2
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Parameters
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v1
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Vector or differential operator
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v2
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-
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Vector or differential operator
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Description
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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.
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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  .
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Also,  is equivalent to Divergence(F).
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Examples
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![with(Student[VectorCalculus])](/support/helpjp/helpview.aspx?si=4462/file05150/math94.png)
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![SetCoordinates(polar[r, theta])](/support/helpjp/helpview.aspx?si=4462/file05150/math105.png)
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![polar[r, theta]](/support/helpjp/helpview.aspx?si=4462/file05150/math108.png)
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![v := RootedVector(root = [1, 2], [a, b])](/support/helpjp/helpview.aspx?si=4462/file05150/math112.png)
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](/support/helpjp/helpview.aspx?si=4462/file05150/math115.png)
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![w := RootedVector(root = [1, 2], [c, d])](/support/helpjp/helpview.aspx?si=4462/file05150/math119.png)
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](/support/helpjp/helpview.aspx?si=4462/file05150/math122.png)
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![F := Vector[column]([[r^2], [theta]], ["r", "theta"], "field")](/support/helpjp/helpview.aspx?si=4462/file05150/math136.png)
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![VectorCalculus[Nabla].F](/support/helpjp/helpview.aspx?si=4462/file05150/math147.png)
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![SetCoordinates(cartesian[x, y, z])](/support/helpjp/helpview.aspx?si=4462/file05150/math154.png)
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![cartesian[x, y, z]](/support/helpjp/helpview.aspx?si=4462/file05150/math157.png)
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| (10) |
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