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Show that the force given by \(\vec F=(2xy + yz^2)\hat i+(x^2+xz^2)\hat j+2xyz\hat k\) will always be conservative. |
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Answer» \(\vec F=(2xy + yz^2)\hat i+(x^2+xz^2)\hat j+2xyz\hat k\) Condition for conservative vector \(\vec ▽\times\vec F=0\) \(\begin{vmatrix}\hat i&\hat j&\hat k\\ \frac{\partial}{\partial x}&\frac{\partial}{\partial y}&\frac{\partial}{\partial z}\\ (2xy+yz^2)&(x^2xz^2)&2xyz\end{vmatrix}\) \(\hat i(2xz-2xz)-\hat j(2yz-2yz)+\hat k(2x + z^2-2x-z^2)\) \(\vec ▽\times\vec F=0\) |
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