Vector field of gradient vector and contour plot

Leo Liu
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Relevant Equations
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1624441288502.png

Given the equation ##\frac{xy} 3##. It is a fact that the gradient vector function is always perpendicular to the contour graph of the origional function. However it is not so evident in the plot above. Any thought will be appreciated.
 
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Leo Liu said:
However it is not so evident in the plot above.
Why do you say that? It looks true to me in the plot.
 
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FactChecker said:
Why do you say that? It looks true to me in the plot.
Some of the level curves are missing. Maybe I should decrease the sampling interval for the level curves?
 
The level curves are all hyperbolas. Try imagining a couple more of them and see if it's crosses through the gradients perpendicularly.
 
Leo Liu said:
Given the equation ##\frac{xy} 3##. It is a fact that the gradient vector function is always perpendicular to the contour graph of the origional function. However it is not so evident in the plot above. Any thought will be appreciated.
##xy/3## is a scalar field, it is not an equation. An equation requires an equal sign.

Apart from that, it is quite apparent from the plot that the gradient is orthogonal to all of the level curves you have provided. I do not understand what more you want from such a plot.
 
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