What Do the Symbols in These Vector Field Equations Represent?

[TFM]

Homework Statement

Determine Div E and Curl E for each of the following vector fields:

$$\vec{E} = (\hat{x} - \hat{z})cos(3(x - z))$$

$$\vec{E} = (\hat{x} + \hat{z})sin(3y)$$

Homework Equations

N/A

The Attempt at a Solution

I can do the div and curl, but I am uncertain what the hat x and y are representing. They normally mean vectors, but I haven't seen them put togther like that? if there was just one letter in hat, I would know that it is, for examle, $$\hat{x}sin(x)$$ the div would be cos(x), but I confused by the two hats together. Any ideas?

TFM

 

[Dick]

Suppose you write it this way instead?
$$\vec{E} = \hat{x} cos(3(x - z))- \hat{z} cos(3(x - z))$$
Is it still confusing? The hats are just the unit vectors.

 

[TFM]

Suppose you write it this way instead?
$$\vec{E} = \hat{x} cos(3(x - z))- \hat{z} cos(3(x - z))$$
Is it still confusing? The hats are just the unit vectors.

Now that makes sense - I knew that they were unit vectors, but I wasn't sure what it meant when they were grouped together like that.

Thanks ,

TFM

 

[TFM]

Just checking my answers...

is the curl of E = 0

and the div E

-sin(3(3x - 3z)) - sin(3()3x - 3z)

TFM