The discussion revolves around the properties of the gradient vector of a scalar field represented by the function ##\frac{xy}{3}## and its relationship to the contour plot of that function. Participants are examining the visual representation of the gradient and its perpendicularity to the contour lines.
The discussion is active, with participants exploring different interpretations of the contour plot and the gradient's properties. Some guidance has been offered regarding the nature of the level curves and their relationship to the gradient, but there is no explicit consensus on the clarity of the plot.
There is a mention of missing level curves in the plot, which may affect the interpretation of the gradient's behavior. Additionally, a clarification is made regarding the nature of the function as a scalar field rather than an equation.
Why do you say that? It looks true to me in the plot.Leo Liu said:
Some of the level curves are missing. Maybe I should decrease the sampling interval for the level curves?FactChecker said:
##xy/3## is a scalar field, it is not an equation. An equation requires an equal sign.Leo Liu said: