To show that it is a gradient vector field by determining the function which satisfies is 9/2z^2-7xy
A movement from one point to another is described by a vector. A vector quantity has a magnitude and a direction (size). There is just magnitude for scalar quantities. An arrow-labeled line segment can serve as a visual representation of a vector.
Zero Vector.
Unit Vector.
Position Vector.
Co-initial Vector.
Like and Unlike Vectors.
Co-planar Vector.
Collinear Vector.
Equal Vector.
We have the field, and so we have all of our potential partial derivatives.
∂V/∂x=−7y
∂V/∂y=−7x
∂V/∂z=9z
Note that to get the mixed derivatives, we need the potential to have
−7xy
That takes care of the first two, to get the last partial we need
And so a potential function is
9/2z^2-7xy
To learn more about vectors click the following link:-
https://brainly.com/question/25705666
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