Discussion Overview
The discussion revolves around the question of why only the dot product and cross product are commonly defined for vector multiplication in physics, while other potential vector products, such as the proposed A#B, are not utilized or required in physical applications. The scope includes theoretical considerations and practical applications in physics and engineering.
Discussion Character
- Debate/contested
- Conceptual clarification
Main Points Raised
- One participant proposes a new vector product, A#B, defined as ABcos@i, questioning its absence in physics and the sufficiency of the dot and cross products.
- Another participant suggests that the initial question becomes obsolete upon defining a new vector product.
- A later reply emphasizes that the dot and cross products are the most useful for solving problems in physics and engineering, particularly in contexts like work done and torque.
- Some participants note that there are indeed other vector products defined, referencing external sources, but imply that these are not commonly encountered in typical physics problems.
- It is mentioned that the dot and cross products are taught first due to their widespread applicability in foundational physics and engineering.
Areas of Agreement / Disagreement
Participants express differing views on the necessity and utility of other vector products beyond the dot and cross products. While some acknowledge the existence of other products, there is no consensus on their relevance or application in standard physical scenarios.
Contextual Notes
Limitations include the potential for other vector products to be useful in specific contexts that are not commonly studied, as well as the dependence on the definitions and applications of vector multiplication in various fields.