Question regarding Curl and Cross Product

AI Thread Summary
The discussion centers on the relationship between the curl in vector calculus and the cross product of the del operator with a vector. The original poster notes a difference in the determinants used in the standard cross product formula versus the curl, specifically mentioning the use of i + j + k for curl. A clarification is provided regarding the determinants, highlighting that while the cofactors are consistent, the order of terms can lead to confusion. The Wikipedia page on curl is referenced, noting a potential misunderstanding due to the arrangement of terms in the formula. The conversation concludes with an acknowledgment of the clarification, enhancing understanding of the curl's computation.
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I'm studying vector calculus, and have a question about the curl and its relation to a cross product of the del operator and a vector. When doing a standard cross product as the formula I have i(det1) - j(det2) + k(det3), where det1, 2 3 are the appropriate 2x2 determinants. However for the curl it's the same determinants, but i + j + k. I'm wondering what the reason for the difference is?
 
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I don't think you are right in your assertion. Curl operates like any other cross product, and the method of cofactors operates the same way.

Looking at the wikipedia page for curl though, you might get confused by the formula given as it has 3 +s, but notice that the order of the ad-bc is switched in front of the j to bc-ad.
 
Ah, I see what I missed now. Thanks for pointing that out.
 
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