We defined a projection onto that line L as a transformation. In the video, we drew it as transformations within R2, but it could be, in general, a transformation from Rn to Rn.

So if you add this blue projection of x to x minus the projection of x, you're, of course, you going to get x. We also know that this pink vector is orthogonal to the line itself, which means it's …

In the last video, we visualized an ethane molecule with a Newman Projection. What I want to do in this video is show that you can really visualize longer chains, or even, we'll see in future …

Let's look at our vertical lines, so this line right here means a bond going away from us in space, so we're staring down at our chiral center, and that's a bond to a carbon and that carbon is …

Here we have pictures of the three eclipsed conformations from the video, and to save time, let's just analyze the pictures and then we'll draw the least stable conformation as a Newman …

Carbon two is in the way, but in our Newman projection, we represent that with a circle, so this circle represents carbon three. And what's attached to carbon three? There's a methyl group …

Now by definition, that right there is the projection of x onto v, and this is the projection of x onto the orthogonal complement of v. So we can write that x is equal to the projection onto v of x, …

When you use the Newman projection, this is only a 60-degree angle. It is gauche to carbon number three. So maybe they're crowding each other a little bit. Let's compare it to the …

And to visualize it a little better, I'll draw what's called a Newman Projection. So I'm going to draw this exact thing, but with a Newman Projection, you draw the carbon molecules directly in front …

Vector A B → shown below has magnitude 3 3 . Find the scalar projection of A B → on the directed line l .