But they won't be the level curves of a function for which this is the gradient.

但它们不一定是，某个以该向量场为梯度的函数的等值线。

youdao

If you look at the separations between consecutive colors, these are the level curves of a function that tells you the temperature at a given point.

如果你们观察在连续颜色之间的分色，那些就是一个函数的等高线，它们告诉你在某一个给定点的温度。

youdao

If the two level curves are tangent to each other that means they have the same tangent line. That means that the normal vectors should be parallel. Let me maybe draw a picture here.

如果两个等高线相切，说明它们的切线相同，也就是说他们的法向量应该平行，我再在这里画个图。

youdao