1 answer:
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Answer:
a)
b)
c) the points of the form (x, -x) for x≠0
Step-by-step explanation:
a)
If φ(x, y) = arctan (y/x), the vector field F = ∇φ would be
On one hand we have,
On the other hand,
So
b)
The domain of definition of F is
i.e., all the plane X-Y except the (0,0)
c)
Here we want to find all the points such that
where k is a real number other than 0.
But this means
So, all the points in the line y = -x except (0,0) are parallel to the vector field F, that is, the points (x, -x) with x≠ 0