- #1
bcjochim07
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Homework Statement
I was reading some notes about the del operator, and they make the statement
∇ x (Ua) = 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 (Ua) = U(∇ x a) + -a x (∇U)
Could somebody help clear my confusion? Thanks.