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I'm trying to prove the identity $$a \times (\nabla \times a) = 1/2\nabla (a^2)-(a\cdot\nabla)a$$ But using the BAC-CAB rule I only get: $$a \times (\nabla \times a) = \nabla (a^2)-(a\cdot\nabla )a$$ I don't know why must be a factor $1/2$ on the right side of the equal sign. Could anyone help me, please?

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