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**1. Homework Statement**

I was reading some notes about the del operator, and they make the statement

∇ x (U

**a**) = U(∇ x

**a**) + (∇U) x

**a**.

However, I disagree with this because it seems to me that in the right hand side of the equation for the second term, the ∇ is operating on

**a**, since

**a**appears after it.

I also worked on some other examples to see if understood the properties of del. For instance, for an arbitrary vector function

**A**and position vector

**r**,

(

**A**dot ∇)

**r**=

**A**and

(

**A**x ∇) dot

**r**= 0.

Both of these examples seem to confirm that ∇ operates on what appears after it (crossed, multiplied, or dotted, but not added or subtracted).

If I expand the right hand side of the above equation, I don't get the left hand side.

I think that the statement should read

∇ x (U

**a**) = U(∇ x

**a**) + -

**a**x (∇U)

Could somebody help clear my confusion? Thanks.

**2. Homework Equations**

**3. The Attempt at a Solution**