• across
A student asked me to prove$\nabla\times\left(\vec F\times\vec G\right)=(\vec G\cdot\nabla)\vec F-(\vec F\cdot\nabla)\vec G+(\nabla\cdot\vec G)\vec F-(\nabla\cdot\vec F)\vec G,$and I ended up having to stop midway through because of how long and tedious the process is. Would someone mind helping me find a proof of it? It's a well-known vector operator identity.
Mathematics

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