User:Emma080404/Vector multiplication

Lead
The content gap I plan to edit is adding vector multiplication that can be applied to engineering. I plan to do that because, in the article, they said that vector multiplication can apply to physics and engineering. They explain the physics part but not the engineering part. My plan is to find a source that talks about vector multiplication applied to engineering and write about that in this article. I also plan to write some more information for dots product and cross product.

Article body
Engineering uses Vector multiplication to analyze, framework the model, and design the complex system. Engineer uses Vector multiplication such as dots product, and cross product to perform the calculation, model the physical object, and take out important relationships that govern various engineering phenomena. It helps the engineer have a deep understanding of how to find the right system and apply the solution in the real world.

The dots product can be distributed like A*(B+C) = A*B +A*C. Also, the cross can be distributed too like Ax(B+C) =(AxB)+ (AxC).

Explanation/Outline
The content gap I plan on filling is that of history. I'll start by creating a section that briefly gives this history with more on a focus on history towards vector multiplication and not so much on everything about vectors. This will over time be expanded to the other concepts that are within vector multiplication. I'll focus in on the scientists/contributions that had the most impact and that lead to the modern notation/equation.

Brief history
A scientist by the name of William Rowan Hamilton is credited with the creation and use of quaternions in 1843, which would be the predecessor to the "modern" form of dot/cross products. Hamilton had also observed what would be the equations of the dot/cross product using quaternions as well. When it comes to the way in which vectors look and work, especially for the dot/cross products, J. Willard Gibbs, Oliver Heaviside, as well as Edwin Bidwell Wilson are credited with this. Gibbs and Heaviside would separately create the cross product in 1881. While the dot product was created in 1901 by Gibbs and Wilson.

Def of vector multiplication (For beginning of article, separate from history)
In mathematics, vector multiplication is the multiplication of a vector to either a scalar or another vector. It includes as a whole the properties of anti-commutativity and distributivity for the operations of it. It may refer to one of several operations between two (or more) vectors. It may concern any of the following articles: