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VectorCalculus

  

*

  

An overloaded version of Star that deals with scalar multiplication of Vectors

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

s*v

Parameters

s

-

algebraic; the scalar to scale the Vector

v

-

Vector(algebraic); the Vector to scale

Description

• 

Returns the scalar multiplication of s and v.

• 

An overloaded version for the VectorCalculus package that deals with scaling Vectors (scalar multiplication) in different coordinate systems.

• 

The following table describes the interaction between different types of Vector objects in different coordinate systems when the Star operator is applied.

 

v

coord(v)

s*v

coord(s*v)

1

free Vector

cartesian

free Vector

cartesian

 

free Vector

curved

error

 

2

rooted Vector(root)

any

rooted Vector (root)

any

3

vector field

any

vector field

any

4

position Vector

cartesian

position Vector

cartesian

• 

Note that in 2-D math, the Star operator appears as a dot.

Examples

withVectorCalculus:

Only free Vectors in cartesian coordinates can be scaled.

21,1,2

v1Vector1,2,coordinates=cartesianx,y

v112

(1)

3v1

Rooted Vectors in any coordinate system can be scaled.

v2RootedVectorroot=1,Pi2,1,2,polarr,t

v212

(2)

3v2

36

(3)

v3RootedVectorroot=1,2,1,1,parabolicu,v

v311

(4)

2v3

22

(5)

Vector Fields in any coordinate system can be scaled.

vfVectorFieldx,y,cartesianx,y

xvf

Position Vectors can be scaled.

pvPositionVectorp,p,polarr,t

pvpcosppsinp

(6)

1pv2

pcosp2psinp2

(7)

See Also

VectorCalculus

VectorCalculus[PositionVector]

VectorCalculus[RootedVector]

VectorCalculus[Vector]

VectorCalculus[VectorField]