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What else can we do with Del?

Since $\nabla$ is almost a vector, we can think of all the ways that we can act on vectors and see how del should respond.

	Vectors	Del
1	Multiply by a scalar, a: $\vec{A}a$	Operate on scalar f: $\nabla f$ (the gradient)
2	Dot product with $\vec{B}$ : $\vec{A} \cdot \vec{B}$	Dot product with $\vec{F}(x,y,z)$ : $\nabla \cdot \vec{F}$
3	Cross product with $\vec{B}$ : $\vec{A} \times \vec{B}$	Cross product on $\vec{F}(x,y,z)$ : $\nabla \times \vec{F}$

The gradient is described in the chapter on derivatives. Below, we discuss the other operations of del.

Vector Calculus
8/19/1998