Now what I'd like to do in this particular lesson is to analyze a particular tetrahedron in which we will be able to describe slip in an FCC material. What I've done is I put together two cubes. And those two cubes are describing the same tetrahedral. The tetrahedral corners are A, B, C and D and what I want to do is to go plane by plane and describe the vectors that define the plane. With the respect to the edges of the plane and the normal to the plane itself, and we'll do this for all the four orientations of the tetrahedron. So, first we'll determine what the direction AC is, the direction AC by using the idea of the origin of our vector to the tip of the vector, we can determine then that this vector is going to be along the 011-bar direction. When I look at the vector AB, it's along the 1-bar 10 direction. If I take those two vectors and I wind up crossing those two vectors, what I'm going to do is to determine the plane ABC. And that has the orientation of 111. Now we move to the cube to the right and we look at the plane that's shadowed here, and now we look at the vector AD. And it goes from position A to position D. And then we do the same thing where we look at the vector that defines the direction AC. And all we have to do is to take those two directions, determine what the cross product of those two directions is, and that will give us the plane one, one bar, one bar. I would suggest that you go by with this illustration and go through and determine those vectors in those planes for yourself. Now we'll look at the remaining two faces of the tetrahedron. One to the left, and that's going to give us our vector, AB. Then we look at the vector along the direction of AD. We take the cross product and now we have defined another of the 111 planes. We come over to the right and we're now looking at the last face. Again we define two vectors in the plane. We take the cross product of those two vectors and we get the vector normal to the plane. So these are the kind of things that I think it's very important for you to describe and be able to calculate through. So when we begin to talk about some more advanced concepts in this chapter you will have all the machinery necessary to do that. Thank you.