Teaching MPPSC Assistant Professor Mock Test Series 2025 Physical Sciences Mathematical Methods of Physics Vector Algebra and Vector Calculus
Consider two scalar function f(x, y, z) and g(x, y, z) and \( \mathbf{r}\) describes a closed curve C . The gradient of any function is defined as \(\vec\nabla f=\frac{\partial f}{\partial x}\hat i +\frac{\partial f}{\partial y}\hat j+\frac{\partial f}{\partial z}\hat k\) . The most appropriate correct option is :
1
0
2
\(\displaystyle \int_C \int_C f \nabla g + g \nabla f \cdot d\mathbf{V} = 0\)
3
\(\displaystyle \int_C f \nabla g + g \nabla f \cdot d\mathbf{r} = 0\)
4
None of the above