1. The problem statement, all variables and given/known data Need to prove that: (v⋅∇)v=(1/2)∇(v⋅v)+(∇×v)×v 2. Relevant equations Vector triple product (a×b)×c=-(c⋅b)a+(c⋅a)b 3. The attempt at a solution I know I could prove that simply by applying definitions directly to both sides. I haven't done that because that is tedious, and I strive for a more elegant proof and thought that triple product would give it to me. Since we are dealing with operators the order of the vectors is important and applying triple product would give me (v⋅∇)v=(v⋅v)∇+(∇×v)×v But it seems to me that (v⋅v)∇≠ (1/2)∇(v⋅v). It can't be right, because (v⋅v)∇still needs to be applied to something, while the left hand of the equation is something definite. And I can't see where the 1/2 should come from. Is it wrong to apply triple product to this problem? How else could I prove this identity? Any help?