What is the difference between cross product and dot product?

i want to know waht is different between cross product and dot product???
and fields at adielectric interface and fields at the interface with a perfect conductor
and what n(the normal unit vector mean????and from where it come

thank u for helping

cross product sample problem electromagnetic

I recommend you read the book "Div Grad Curl and All That" by H.M. Schey. It is short, not too mathy, and will help give you a very strong foundation in when and how to apply Dot and Cross products. It also covers unit norms.

I read it as an undergrad and it clarified everything more than any tutor ever did.

div grad curl and all that google

**broken link removed**
i tried to download it from here but when i finshed i did know how can i read it ( with which program)

can u help me plz

div, grad, curl and all that djvu

rar is a compression format (like zip files). Google around and you can find a free unzipper (or rather unrarer). The book is a .djvu format, the reader for which can be downloaded from djvu.org for free.

Looking through it, it occurs to me that this may possibly be too much. I'll try to answer your three questions directly here, and maybe the book can offer further insight.

Added after 35 minutes:

A unit norm isn't too bad. Think of a line that you draw on a piece of paper, then choose any point on that line. If I then asked you to draw another line that is perpendicular to the first and also passed through the same point, you can easily see that there is only one line that you can possibly draw that will satisfy both requirements.

Now picture the same problem, only now the line is pointing straight up out of the page. Now if I asked you to draw a line, it isn't as clear. For example, a line that extends in a North-South direction would be a right angles to the line facing directly upward. However, a line that faces East-West would also be.

If you think for just a bit, you will see that there are in fact infinitely many lines which could intersect the line pointing straight upwards at the same point.

If you lumped all of those lines together, you see that you end up with a plane. In fact, this is a common way to mathematically define a plane. It goes like this:

Define a line segment (i.e. a vector). In this case, our line points straight upward, so I will say that it points [0 0 1]. I made the line of length 1 so that it is of "unit" length.

Now pick a point that you want your plane to pass through. Lets say three feet off the floor, or (0, 0, 3)

Now lets pick another arbitrary point (x, y, z). How can I tell if this point is on the plane? Well, the line that passes through this point would also have to pass through our reference point AND be perpendicular to our reference unit norm. The line can be defined as [(x, y, z) - (0, 0 ,3)] which becomes [x, y, z-3]

How can I tell if this is perpendicular to the other line? This is where the dot product comes in. The Dot product is a mathematical tool for determining the degree to which two vectors are parallel. Since we are looking for perpendicular, we actually want there be no element of being parallel at all, i.e. the dot product is zero.

To perform the dot product, multiply each component of our two vectors and add them up. For our case, we have
[0 0 1] (dot) [x, y, z-3] = 0

Any point (x, y, z) that satisfies this relationship will be on our plane. Performing the multiplication yields,
0*x + 0*y + 1*(z-3) = 0

which results in the requirement z = 3. Thus, the point (x, y, 3) will lie on our plane for any x or y.

This also raises the idea of why it is good to use a reference line that has a length of 1, or unit norm. Suppose instead we use a longer line, such as [0 0 5]. Working the problem results in a final step of
[0 0 5] (dot) [x, y, z-3] = 0
5*(z-3)=0
5z = 15
z = 3

Note that our first problem was automatically in simplest form, whereas this time we had to do an extra step of cancellation to simplify the problem. As you work more difficult problems, you will find that defining the norm as unit length makes the math much easier to handle.

This example is very simple, and I will try to work one that is a little more involved. Please let me know i this is helpful and specific questions this raises.

div, grad, curl, and all that download

Your questions were essential questions, but in short I just can tell you that at products which we expect a vector in output we use cross product and otherwise we use dot product. And about your second question, fields at a dielectric interface can be determined by maxwell equations but ideally there isn't any field at the interface with a perfect conductor.
Have a good time!!