XL: Visual Basic Function to Calculate Cross Product

• Microsoft Excel for Windows, versions 5.0, 5.0c
• Microsoft Excel for the Macintosh, versions 5.0, 5.0a
• Microsoft Excel for Windows NT, version 5.0
• Microsoft Excel for Windows 95, versions 7.0, 7.0a
• Microsoft Excel 97 for Windows
• Microsoft Excel 98 Macintosh Edition

SUMMARY

This article contains a sample Microsoft Visual Basic for Applications function that takes two arrays (three rows by one column) of numbers, each representing a vector, and returns an array of the same dimensions representing the cross product of the two vectors.

MORE INFORMATION

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            i   j   k
            =========
c = a x b = m   n   o  = [(n*z)-(o*y)]i - [(o*x)-(m*z)]j + [(m*y)-(n*x)]k
            x   y   z

   a = (1,2,3)
   b = (4,5,6)

   c = [(2*6)-(3*5)]i - [(3*4)-(1*6)]j + [(1*5)-(2*4)]k
     = [12-15]i - [12-6]j + [5-8]k
     = [-3]i - [6]j + [-3]k
     = (-3,6,-3)

Sample Visual Basic Procedure

   ' The following line must be placed at beginning of module:
   Option Base 1

   ' Returns the cross product of the two input vectors.
   Function Cross_Product_VBA(Vec1 As Object, Vec2 As Object) As Variant

       ' TempArray is a temporary variable to store the cross product.
       Dim TempArray(3, 1)

       ' The following lines put elements of the product into TempArray.
       TempArray(1, 1) = Vec1.Cells(2, 1).Value * _
           Vec2.Cells(3, 1).Value - Vec1.Cells(3, 1).Value * _
           Vec2.Cells(2, 1).Value
       TempArray(2, 1) = Vec1.Cells(3, 1).Value * _
           Vec2.Cells(1, 1).Value - Vec1.Cells(1, 1).Value * _
           Vec2.Cells(3, 1).Value
       TempArray(3, 1) = Vec1.Cells(1, 1).Value * _
           Vec2.Cells(2, 1).Value - Vec1.Cells(2, 1).Value * _
           Vec2.Cells(1, 1).Value

       ' Assigns the TempArray variable to Cross_Product_VBA.
       Cross_Product_VBA = TempArray

   End Function

   =Cross_Product_VBA(A1:A3,B1:B3)

   A1: 1     B1: 4     C1: -3
   A2: 2     B2: 5     C2:  6
   A3: 3     B3: 6     C3: -3