One important application of a norm of a vector is sometimes we have a vector but we really don't want to work with it until its a unit size. We want the length of the vector to be one. A lot of applications require this, or it makes the problem and application easier if it's done first. We have a vector here, v, going forward from this class in Data Science, or deal with linear algebra. Traditionally u, is the letter denoted for the unit vector. Now this isn't always the case. In previous lessons, I've used the letter u to denote a vector that was not a unit vector. It's not always true. Just keep in mind that sometimes if you see u in the context of linear algebra, they're implying that they want a unit vector, or they're implying that they're giving you a unit vector. Just keep that in mind going forward. If we have any vector v, and we want to keep the directionality and dimension of the vector, but we want the norm or the length of the vector to change to one so we can work with it in a different application. What we do is we make it a unit vector by dividing by the norm of the vector, which we learned what this was last unit and how to calculate it. Then we just multiply that by v. Essentially what we're doing is we're taking the vector that we have and we're dividing by its length and that'll give us a length of one. Then we'll keep the attributes of the vector, it's directionality in the dimensional space. We'll just downsize or upsize it to become a unit vector of length one. I'm not sure if I even said what a unit vector was, but it's just a vector of length one. In this case, we have v here and we want to get this, the norm of v which we learned last time. The norm of v is the square root of v1 plus v2. In this case, we have four values, v3 plus v4. We just need to remember the square each one of them. We know why they're each squared. We did the math of it last time. In this case, we have the square root of 1 squared is 1. Negative 2 squared will give me 4 plus 2 squared will give me 4 again plus 0 squared, which is 1, 4, 4. We add them up, we get 9. This is equal to 3. Square root of 9 will give me 3. U, the unit vector associated with this original vector is 1 divided by 3 times my original vector, 1, negative 2, 2, 0, and that will give me new vector, 1/3, negative 2/3, 2/3, and 0. I've taken v, which is a vector of any length, even if it's already a unit vector, if you do this operation on it, you'll simply get 1 divided by 1 times v and it'll stay the same, which makes sense. It should make sense to you at least. If it doesn't spend a second with it or some time with it. But if I'm given any vector and I want to make it into a unit vector of length one, this is how you do it.