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I'm following a course on vector calculus and I'm having some trouble connecting things. Suppose we have a three-dimensionale vectorfield F(x,y,z)=(F1,F2,F3) and suppose we have a potential phi for this. So: F=grad(phi).

The field lines of a vector field are defined as d(r)/dt = lamba(t)F(r(t)). In words: the derivative of the field line (which is parametrized bij r) is parallel to F(r(t)).

Now for my question. Suppose we have equipotential lines, so phi=c with c a constant. What's the connection between these equipotential lines, the field lines and the vector field in terms of being parallel or right-angled?

I think the answer should be that the field lines are right-angled with the equipotential lines, but I don't know how to deduce this.

Thanks in advance!