Question regarding Curl and Cross Product

[bitrex]

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?

 

[n1person]

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.

 

[bitrex]

Ah, I see what I missed now. Thanks for pointing that out.