How to Calculate a Cross Product in Excel

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Assuming we have vector A with elements (A₁, A₂, A₃) and vector B with elements (B₁, B₂, B₃), we can calculate the cross product of these two vectors as:

Cross Product = [(A₂*B₃) – (A₃*B₂), (A₃*B₁) – (A₁*B₃), (A₁*B₂) – (A₂*B₁)]

For example, suppose we have the following vectors:

• Vector A: (1, 2, 3)
• Vector B: (4, 5, 6)

We could calculate the cross product of these vectors as:

• Cross Product = [(A₂*B₃) – (A₃*B₂), (A₃*B₁) – (A₁*B₃), (A₁*B₂) – (A₂*B₁)]
• Cross Product = [(2*6) – (3*5), (3*4) – (1*6), (1*5) – (2*4)]
• Cross Product = (-3, 6, -3)

The following example shows how to calculate this exact cross product in Excel.

Example: Calculating Cross Product in Excel

To calculate the cross product between two vectors in Excel, we’ll first input the values for each vector:

Next, we’ll calculate the first value of the cross product:

Then we’ll calculate the second value:

Lastly, we’ll calculate the third value:

The cross product turns out to be (-3, 6, -3).

This matches the cross product that we calculated by hand earlier.

Additional Resources

How to Calculate the Dot Product in Excel
How to Calculate a Dot Product on a TI-84 Calculator