Prove that F is conservative iff it is irrotational. That is F is conservative then it is irrotational and if F is irrotational then it is conservative. The 1st part is easy to show. In the second part, I have shown that ∂F_3/∂y=∂F_2/∂z. Similarly the other two partial derivatives are equal. How does one show that Φ is the scalar potential associated with F i.e. F= gradΦ?
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Welcome to [math.se] SE. Take a [tour]. You'll find that simple "Here's the statement of my question, solve it for me" posts will be poorly received. What is better is for you to add context (with an [edit]): What you understand about the problem, what you've tried so far, etc.; something both to show you are part of the learning experience and to help us guide you to the appropriate help. You can consult this link for further guidance. – Another User May 03 '23 at 10:32
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Thank you. I have mentioned uptill where I was able to think about the proof. I hope the minor edits that I've made to the question fits in well with your advice. – Tejashree May 03 '23 at 17:40
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Does this answer your question? Necessary and sufficient for vector field to be conservative – Kurt G. May 03 '23 at 19:01
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I'm not sure as I'm not well versed with the concepts mentioned there. I'm still learning the basics of vector calculus and calculus as a subject in general. Thank you though! – Tejashree May 04 '23 at 14:56