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nathangrand
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Show the following, where U is a vector, and r is the position vector: \nabla(U.r) = U in polar coordinates
Many Thanks
Many Thanks
An easy vector identity I can't prove
- Thread starter nathangrand
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SUMMARY
The discussion centers on proving the vector identity \nabla(U.r) = U in polar coordinates, where U represents a vector and r denotes the position vector. Participants highlight the necessity of starting with the basis vectors to approach the proof effectively. A mechanical check indicates that the initial assumption of "find U such that..." may not be valid. The conversation emphasizes the importance of a structured approach in vector calculus.
PREREQUISITES- Understanding of vector calculus principles
- Familiarity with polar coordinates
- Knowledge of gradient operations in vector fields
- Experience with basis vectors in vector spaces
- Study the properties of gradient operations in vector calculus
- Explore the derivation of vector identities in polar coordinates
- Learn about basis vectors and their applications in vector analysis
- Investigate common mistakes in vector identity proofs
Mathematicians, physics students, and anyone involved in vector calculus or related fields will benefit from this discussion, particularly those looking to deepen their understanding of vector identities and polar coordinates.
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