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This is the application of Lagrange multiplier.

Is this solution true? If there exist a little bit mistake in detail of the answer, please tell me to correcting this.

Sorry for adding photo. I dont have enough ability to write this as MathJax.

Hopefully, Photos are readable.

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Mahdi Khosravi
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  • In your answer to question $1$ you wrote that $\nabla f\times\nabla g$ is the determinant of a 2 by 3 matrix. This is not true. The output of the determinant is a real number and the output out the cross product is a vector. Even worse the determinant is not defined on 2 by 3 matrices. I think you were thinking of a nmemonic used to remember the components of the cross product. To get the conclusion of question $1$ simply write out the components of the cross product and the conclusion follows immediately. – user71352 Jul 28 '13 at 01:12

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