Cross products vs. dot products

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SUMMARY

Cross products and dot products are fundamental operations in vector mathematics. The cross product of two vectors results in a new vector that is orthogonal to the original vectors, commonly used to calculate moments (M = r x F). In contrast, the dot product yields a scalar value, which is utilized to determine the work done by a force (W = F d). Understanding these operations is essential for applications in physics and engineering.

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Joyci116
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I have a question regarding cross products and dot products. What is the difference, and are there any similarities? What ARE cross products and what are their functions? What ARE dot products and what are their functions? What do we use them for?

Thank you,

Joyci116
 
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Joyci116 said:
I have a question regarding cross products and dot products. What is the difference, and are there any similarities? What ARE cross products and what are their functions? What ARE dot products and what are their functions? What do we use them for?

Thank you,

Joyci116

Well, first of all, you use cross products and dot products when you work with vectors, and I would say (at least how I convinced myself) they are something made up by mathematicians to make vectors useful.

A cross product between two vectors products another vector that is orthogonal to the original two. For example, cross product can be used to find the moment:

M = r x F

A dot product, on the other hand, between two vectors produces a scalar, basically a number. Dot product can be used to calculate the work done by a force:

W = F d

P.S. The bold letters are vectors, and the unbold ones are scalar.
 
So what you are trying to convey is that you multiply with cross products and dot products, but it is WHAT you multiply determines whether it is a dot or cross product? Scalar is always dot and vector is always cross product?
 

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