VectorCalculus - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Vector Calculus : VectorCalculus/CrossProduct

VectorCalculus

  

CrossProduct

  

computes the cross product of Vectors and differential operators

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

CrossProduct(v1,v2)

v1 &x v2

Parameters

v1

-

Vector(algebraic); Vector, Vector-valued procedure, or differential operator

v2

-

Vector(algebraic); Vector, Vector-valued procedure, or differential operator

Description

• 

The CrossProduct(v1, v2) function (vector product) computes the cross product of v1 and v2, where v1 and v2 can be either three dimensional free Vectors, rooted Vectors, position Vectors, vector fields, Del or Nabla.

• 

The function  and can be accessed through  &x or CrossProduct exports.

• 

The behavior of cross product is contained in the following table

 

v1

coord (v1)

v2

coord (v2)

v1 &x v2

coord (v1 &x v2)

1

free Vector

cartesian

free Vector

cartesian

free Vector

cartesian

 

free Vector

curved

free Vector

any

error

 

2

free Vector

cartesian

rooted Vector (root2)

coord2

rooted Vector (root2)

coord2

3

free Vector

any

vector field

any

error

 

4

free Vector

cartesian

position Vector

cartesian

free Vector

cartesian

 

free Vector

curved

position Vector

cartesian

error

 

5

rooted Vector (root1)

coord1

rooted Vector (root1)

coord1

rooted Vector

coord1

 

rooted Vector (root1)

coord1

rooted Vector (root2)

coord1

error

 

 

rooted Vector (any)

coord1

rooted Vector (any)

coord2

error

 

6

rooted Vector (root1)

coord1

vector field

coord2

v1 &x v2root1

coord2

7

rooted Vector (root1)

cartesian

position Vector

cartesian

rooted Vector (root1)

cartesian

8

vector field

coord1

vector field

coord1

vector field

coord1

 

vector field

coord1

vector field

coord2

error

 

9

vector field

coord1

position Vector

cartesian

error

 

10

position Vector

cartesian

position Vector

cartesian

position Vector

cartesian

Examples

restart

withVectorCalculus:

Take the cross product of two free Vectors in cartesian coordinates.

1,0,0 &x 0,1,0

ez

(1)

v1Vector1,4,0,coordinates=cartesianx,y,z

v1:=ex+4ey

(2)

v2Vector1,1,1,coordinates=cartesianx,y,z

v2:=ex+ey+ez

(3)

CrossProductv1,v2

4exey3ez

(4)

GetCoordinatesCrossProductv1,v2

cartesianx,y,z

(5)

Take the cross product of two rooted vectors if they have the same coordinate system and root point.

vsVectorSpace1,π3,π3,sphericalr,p,t

vs:=modulelocal_origin,_coords,_coords_dim;exportGetCoordinates,GetRootPoint,Vector;end module

(6)

v1RootedVectorroot=vs,1,1,1

v1:=111

(7)

v2RootedVectorroot=vs,1,0,1

v2:=101

(8)

v1 &x v2

101

(9)

GetRootPointv1 &x v2

er+13πep+13πet

(10)

The cross product of a cartesian free Vector and a rooted Vector is valid. The resulting Vector is rooted.

v1RootedVectorroot=1,π4,1,1,1,1,cylindricalr,p,h

v1:=111

(11)

v2Vector0,0,1,coordinates=cartesianx,y,z

v2:=ez

(12)

v2 &x v1

110

(13)

GetRootPointv2 &x v1

er+14πep+eh

(14)

GetCoordinatesv2 &x v1

cylindricalr,p,h

(15)

The cross product of two vector fields is defined if they are in the same coordinate system.

vf1VectorFieldr,φ,θ,sphericalr,φ,θ

vf1:=re_r+φe_φ+θe_θ

(16)

vf2VectorFieldr2,φ,φ,sphericalr,φ,θ

vf2:=r2e_r+φe_φ+φe_θ

(17)

CrossProductvf1,vf2

φ2φθe_r+r2θφre_φ+φr2+φre_θ

(18)

Use differential operators to compute the Curl of a vector field.

FVectorField1,x,y,cartesianx,y,z

F:=e_xxe_y+ye_z

(19)

Del &x F

e_xe_z

(20)

GVectorFieldr,t,p,sphericalr,p,t

G:=re_r+te_p+pe_t

(21)

Del &x G

rcospp+rsinprr2sinpe_rpre_p+tre_t

(22)

The cross product of two position Vectors is defined. The result is a position Vector.

pv1PositionVector1,p,q,sphericalr,φ,θ

pv1:=sinpcosqsinpsinqcosp

(23)

pv2PositionVector1,p,p,cylindricalr,φ,h

pv2:=cospsinpp

(24)

CrossProductpv1,pv2

sinpsinqpcospsinpsinpcosqp+cosp2sinp2cosqsinpsinqcosp

(25)

AboutCrossProductpv1,pv2

Type: Position VectorComponents: sinpsinqpcospsinp,sinpcosqp+cosp2,sinp2cosqsinpsinqcospCoordinates: cartesianRoot Point: 0,0,0

(26)

See Also

LinearAlgebra[CrossProduct]

VectorCalculus

VectorCalculus[Curl]

VectorCalculus[Del]

VectorCalculus[PositionVector]

VectorCalculus[RootedVector]

VectorCalculus[Vector]

VectorCalculus[VectorField]

 


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam