Well, we've seen this criterion that if a curl of the vector field is zero and it's defined in the entire plane, then the vector field is conservative, and it's a gradient field.

我们已经知道了一个准则，如果向量场的旋度为零，而且它在整个平面上有定义，那么这个向量场是保守的，而且它是个梯度场。

youdao

I have a curve in the plane and I have a vector field.

这有一条平面曲线和一个向量场。

youdao

Now, an important difference between curl here and curl in the plane is that now the curl of a vector field is again a vector field.

和平面上的旋度的一个重要的不同点是，这里向量场的旋度，仍然是一个向量场。

youdao