In Marion & Thorton problem 1.29 asks to find the angle between two surfaces [tex](x^2 +y^2 + z^2)^2 = 9[/tex] and [tex]x + y + z^2 = 1[/tex] at a point.(adsbygoogle = window.adsbygoogle || []).push({});

The solution takes the gradient of [tex](x^2 +y^2 + z^2)^2 - 9[/tex] and [tex]x + y + z^2 - 1[/tex], and using the dot product between the two vectors at that point gets the angle.

My question is, isn't [tex](x^2 +y^2 + z^2)^2 - 9[/tex] and [tex]x + y + z^2 - 1[/tex] both zero and hence taking the gradient would give you 0. shouldn't you rather take one variable as the dependent variable so you have z(x,y) for example and then take the gradient of that? I'm confused as to why they took the gradient of the way they did.

Thanks for your help.

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# Angle between two surfaces and gradient

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