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VectorCalculus[*] - An overloaded version of Star that deals with scalar multiplication of Vectors
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Parameters
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s
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-
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algebraic; the scalar to scale the Vector
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v
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Vector(algebraic); the Vector to scale
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Description
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Returns the scalar multiplication of s and v.
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An overloaded version for the VectorCalculus package that deals with scaling Vectors (scalar multiplication) in different coordinate systems.
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The following table describes the interaction between different types of Vector objects in different coordinate systems when the Star operator is applied.
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coord( )
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coord( * )
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1
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free Vector
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cartesian
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free Vector
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cartesian
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free Vector
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curved
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error
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2
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rooted Vector(root)
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any
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rooted Vector (root)
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any
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3
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vector field
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any
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vector field
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any
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4
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position Vector
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cartesian
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position Vector
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cartesian
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Note that in 2-D math, the Star operator appears as a dot.
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Examples
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Only free Vectors in cartesian coordinates can be scaled.
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![Vector[column]([[2], [2], [4]], ["x", "y", "z"])](/support/helpjp/helpview.aspx?si=4980/file03358/math187.png)
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![v1 := Vector(`<,>`(1, 2), coordinates = cartesian[x, y])](/support/helpjp/helpview.aspx?si=4980/file03358/math191.png)
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![v1 := Vector[column]([[1], [2]], ["x", "y"])](/support/helpjp/helpview.aspx?si=4980/file03358/math194.png)
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![Vector[column]([[3], [6]], ["x", "y"])](/support/helpjp/helpview.aspx?si=4980/file03358/math201.png)
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Rooted Vectors in any coordinate system can be scaled.
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![v2 := RootedVector(root = [1, (1/2)*Pi], [1, 2], polar[r, t])](/support/helpjp/helpview.aspx?si=4980/file03358/math207.png)
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](/support/helpjp/helpview.aspx?si=4980/file03358/math210.png)
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](/support/helpjp/helpview.aspx?si=4980/file03358/math217.png)
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![v3 := RootedVector(root = [1, 2], [1, 1], parabolic[u, v])](/support/helpjp/helpview.aspx?si=4980/file03358/math221.png)
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](/support/helpjp/helpview.aspx?si=4980/file03358/math224.png)
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](/support/helpjp/helpview.aspx?si=4980/file03358/math231.png)
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Vector Fields in any coordinate system can be scaled.
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![vf := VectorField(`<,>`(x, y), cartesian[x, y])](/support/helpjp/helpview.aspx?si=4980/file03358/math237.png)
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![vf := Vector[column]([[x], [y]], ["x", "y"], "field")](/support/helpjp/helpview.aspx?si=4980/file03358/math240.png)
| (8) |
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![Vector[column]([[x^2], [x*y]], ["x", "y"], "field")](/support/helpjp/helpview.aspx?si=4980/file03358/math247.png)
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Position Vectors can be scaled.
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![pv := PositionVector([p, p], polar[r, t])](/support/helpjp/helpview.aspx?si=4980/file03358/math253.png)
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], [p*sin(p)]])](/support/helpjp/helpview.aspx?si=4980/file03358/math256.png)
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*p*cos(p)], [(1/2)*p*sin(p)]])](/support/helpjp/helpview.aspx?si=4980/file03358/math263.png)
| (11) |
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