XL: Visual Basic Function to Calculate Cross Product

ID: Q121820

The information in this article applies to:

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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   http://www.microsoft.com/support/supportnet/refguide/

The cross product, c = a x b, of the vectors a and b is a vector that is perpendicular to the plane of a and b. It can be illustrated by the following table:

            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

For example, given two vectors a and b:

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

vector c can be computed:

   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)

In Microsoft Excel, you can create a Visual Basic function to perform these calculations and return the results into an array.

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

Be sure to select three vertical cells before typing the function, and enter the function as an array formula by pressing CTRL+SHIFT+ENTER or COMMAND+RETURN. For example, given the ranges A1:A3 (vector a) and B1:B3 (vector b), calculate the cross product by highlighting C1:C3, type the following function, and press CTRL+SHIFT+ENTER or COMMAND+RETURN:

   =Cross_Product_VBA(A1:A3,B1:B3)

The results are shown below:

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

Additional query words: 5.00 7.00 XL98 XL97 XL7 XL5

Keywords          : kbprg kbdta kbdtacode PgmOthr PgmHowto xlformula KbVBA 
Version           : WINDOWS:5.0,5.0a,5.0c,7.0,97; MACINTOSH:5.0,98
Platform          : MACINTOSH WINDOWS
Issue type        : kbhowto

Last Reviewed: May 17, 1999