Student[MultivariateCalculus]
CrossProduct
return the cross product of two vectors
Calling Sequence
Parameters
Description
Examples
Compatibility
CrossProduct(u, v)
u &x v
u, v
-
three-dimensional Vectors with algebraic entries
The CrossProduct command computes the cross product of u and v.
The infix operator &x can also be used to compute the cross product.
The cross product of u and v is given by the formula u2v3−u3v2,−u1v3+u3v1,u1v2−u2v1.
If u and v are both row Vectors, a row Vector is returned. Otherwise, a column Vector is returned.
withStudent:-MultivariateCalculus:
u≔a,b,c
u≔abc
v≔d,e,f
v≔def
CrossProductu,v
bf−ce−af+cdae−bd
The cross product is anticommutative.
v&xu
−bf+ceaf−cd−ae+bd
The cross product is not associative.
w≔g,h,i
w≔ghi
simplifyu&xv&xw
−af+cdi−ae−bdh−bf+cei+ae−bdgaf−cdg+bf−ceh
−be−cfg+bh+cid−ad−cfh+ag+cie−ad−bei+ag+bhf
The Student[MultivariateCalculus][CrossProduct] command was introduced in Maple 2016.
For more information on Maple 2016 changes, see Updates in Maple 2016.
See Also
Student
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