Vector Analysis Help: #4 & #10

In summary, the conversation discusses the difficulties the speaker is having with problems 4 and 10. For problem 4, they attempted to use the product rule and hints to find a solution, but were unsuccessful. For problem 10, they tried to use identities for divergence and curl found in their textbook, but still struggled with finding a solution.
  • #1
Shackleford
1,656
2
I'm honestly totally clueless on 4 and 10. For #4a, I plugged in dN/ds and used the product but didn't see a solution. I did something similar for 4b. I also don't see how the two hints help. For 10, I multiplied f and the two vectors, tried to find the divergence, used the product rule twice, I believe. Sorry I don't have my notes scanned for these two.

10.jpg


4.jpg


Here are some notes related to #4, I imagine.

untitled-1.jpg


untitled2.jpg
 
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  • #2
The hints for 4a and 4b suggest you differentiate those expressions (the ones in the hints) with respect to s.

For problem 10, you want to use the identities for [tex]\nabla\cdot(f\vec{A})[/tex] and [tex]\nabla\times(f\vec{A})[/tex]. They should be in your textbook somewhere.
 
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FAQ: Vector Analysis Help: #4 & #10

1. What is vector analysis?

Vector analysis is a branch of mathematics that deals with the properties and behavior of vectors. Vectors are mathematical objects that have both magnitude (size) and direction, and are commonly used in physics and engineering to represent physical quantities such as velocity, force, and acceleration.

2. How is vector analysis used in science?

Vector analysis is used in science to analyze and describe physical phenomena in terms of vectors. This includes calculating forces and motion in mechanics, studying electric and magnetic fields in electromagnetism, and analyzing fluid flow in fluid dynamics.

3. What are some common vector operations?

Some common vector operations include addition, subtraction, multiplication by a scalar, dot product, and cross product. Addition and subtraction of vectors involve combining or separating their magnitudes and directions, while multiplication by a scalar changes the magnitude of the vector. The dot product is a way of finding the angle between two vectors, while the cross product results in a new vector perpendicular to the two original vectors.

4. What is the significance of understanding vector analysis?

Understanding vector analysis is essential for solving many problems in physics and engineering. It allows us to break down complex physical phenomena into simpler vector quantities, making it easier to analyze and solve problems. Additionally, many mathematical concepts and techniques used in vector analysis are applicable to other areas of science and mathematics.

5. Are there any resources available for learning vector analysis?

Yes, there are many resources available for learning vector analysis, such as textbooks, online tutorials, and video lectures. It is also recommended to practice solving problems and applying concepts to gain a better understanding of vector analysis. Your local library or university may also offer courses or workshops on the subject.

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