![]() ![]() We are going to use this sequence shortcut during the development our VBA custom function a later section of this article. The 3rd group (z) is adding 1 to each number in the 2nd group: 12 minus 21.The 2nd group (y) is adding 1 to each number: 31 minus 13.In order to remember this sequence for calculating the 3 components for such an end point, you can memorize the mnemonics “xyzzy” or “12332”, which means: Here, ((a2b3 – a3b2), (a3b1 – a1b3), (a1b2 – a2b1)) is actually the end point of the cross product vector. Lastly, we further expand it with cofactor expansion: Next, the matrix can be expanded with Sarrus’s Rule into: The product of vectors a and b can be presented in matrix form as below (also known as a “format determinant”): In this article, let’s sick with the 1-2-3 convention as it’ll make working in Excel easier.) (Note: some people may be more used to reading a x, a y and a z instead, which represent the vector components along the xyz axes. ( a 1, a 2 and a 3 are vector components of a, and b 1, b 2, b 3 are vector components of b.) We have two vectors a and b, where i, j, k are standard basis vectors. Let’s begin with a quick recap of the basics of the math operation for the multiplication of two vectors in a three-dimensional space. Math Recap – Cross Products with 3D Components of Vectors
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