Vector field of gradient vector and contour plot

[Leo Liu]

Homework Statement

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Relevant Equations

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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.

 

[FactChecker]

However it is not so evident in the plot above.

Why do you say that? It looks true to me in the plot.

 

[Leo Liu]

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?

 

[Office_Shredder]

The level curves are all hyperbolas. Try imagining a couple more of them and see if it's crosses through the gradients perpendicularly.

 

[Orodruin]

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.