# An easy vector identity I can't prove

• nathangrand
In summary, to prove the vector identity, one can use basic vector operations and geometric interpretations. The purpose of this identity is to simplify calculations involving vectors in various applications. It can be used for both 2D and 3D vectors and there are alternative ways to prove it. This identity can be applied in research and experiments to simplify calculations and improve efficiency and accuracy.
nathangrand
Show the following, where U is a vector, and r is the position vector: $\nabla$(U.r) = U in polar coordinates

Many Thanks

A quick mechanical check shows it is not right

assuming, "find U such that...", i would start with the basis vectors.

## 1. How can I prove the vector identity?

To prove the vector identity, you can start by writing out the definition of the identity and then manipulating both sides using basic vector operations, such as addition, subtraction, scalar multiplication, and cross or dot products. You can also try using geometric interpretations and properties of vectors to prove the identity.

## 2. What is the purpose of this vector identity?

The purpose of this vector identity is to simplify and streamline calculations involving vectors. By proving and understanding this identity, you can use it in various mathematical and scientific applications, such as mechanics, electromagnetism, and quantum mechanics.

## 3. Can this identity be used for both 2D and 3D vectors?

Yes, this vector identity is applicable for both 2D and 3D vectors. It is a general identity that can be used for vectors in any dimensional space as long as the basic properties of vectors hold true.

## 4. Are there any alternative ways to prove this vector identity?

Yes, there are alternative ways to prove this vector identity. You can try using different mathematical techniques, such as induction, contradiction, or mathematical induction. You can also look for existing proofs or ask for help from other mathematicians or scientists.

## 5. How can I apply this vector identity in my research or experiments?

This vector identity can be applied in various ways in research and experiments. For example, it can be used to simplify calculations involving forces, velocities, and accelerations in mechanics experiments. In electromagnetic experiments, it can be used to simplify calculations involving electric and magnetic fields. Understanding and utilizing this identity can help make your research or experiments more efficient and accurate.

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