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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

with(VectorCalculus):

Only free Vectors in cartesian coordinates can be scaled.

2*<1,1,2>;

2ex&plus;2ey&plus;4ez

(1)

v1:= Vector(<1,2>, coordinates=cartesian[x,y]);

v112

(2)

3*v1;

3ex&plus;6ey

(3)

Rooted Vectors in any coordinate system can be scaled.

v2 := RootedVector(root=[1,Pi/2], [1,2], polar[r,t]);

v212

(4)

3*v2;

36

(5)

v3 := RootedVector(root=[1,2], [1,1], parabolic[u,v]);

v311

(6)

2*v3;

22

(7)

Vector Fields in any coordinate system can be scaled.

vf:= VectorField(<x,y>, cartesian[x,y]);

vfxe&lowbar;x&plus;ye&lowbar;y

(8)

x*vf;

x2e&lowbar;x&plus;xye&lowbar;y

(9)

Position Vectors can be scaled.

pv := PositionVector([p,p], polar[r,t]);

pvpcosppsinp

(10)

(1/2)*pv;

pcosp2psinp2

(11)

See Also

VectorCalculus

VectorCalculus[PositionVector]

VectorCalculus[RootedVector]

VectorCalculus[Vector]

VectorCalculus[VectorField]