Visual Basic Function to Calculate Cross Product

MORE INFORMATION

Microsoft provides programming examples for illustration only, without warranty either expressed or implied. This includes, but is not limited to, the implied warranties of merchantability or fitness for a particular purpose. This article assumes that you are familiar with the programming language that is being demonstrated and with the tools that are used to create and to debug procedures. Microsoft support engineers can help explain the functionality of a particular procedure, but they will not modify these examples to provide added functionality or construct procedures to meet your specific requirements. 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: The results are shown below:

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