Understanding the Laplacian Operator: ∇(∇ * q) vs. Other Operations

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The expression ∇(∇ * q) is discussed in relation to its equivalence to the Laplacian operator. It is suggested that the first nabla represents a dot product, leading to the interpretation as grad(div(q)). The outcome is identified as the Laplacian plus additional terms. These additional terms include curl(curl(q)), indicating a more complex relationship. Understanding this distinction is crucial for applications in vector calculus and differential equations.
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∇(∇ * q) does this equal the laplacian or something else?
 
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I'm going to guess that's supposed to be a dot product on the first nabla? That makes it grad(div(q)). It's equal to the laplacian plus some other stuff. The other stuff is curl(curl(q)).
 

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