### Video Transcript

The components of the vector ๐ฎ are one, two as a terminal point of the vector is one unit right of the initial point and two units up from the initial point. What are the components of the vector ๐ฏ?

The preamble to this question talks about the vector ๐ฎ, which we can see represented in our diagram. And weโre told that the components of this vector are one, two. The components of a vector are written much like the coordinates of a point. They are two numbers which are separated by a comma.

The difference is that the components of a vector are written inside angled brackets and not parentheses as we have for coordinates. Letโs talk about the numbers inside the brackets, the first number is called the ๐ฅ-component. Again, the analogy with points and coordinates is clear.

And the ๐ฅ-component of the vector ๐ฎ is one as the terminal point of the vector is one unit right of the Initial point. And by looking at the diagram, we can see that this is true. The second number inside the brackets is called the ๐ฆ-component of the vector. Its value is two because the terminal point is two units up from the initial point.

And again this is something that we can see by looking at the diagram. We want to find the components of the vector ๐ฏ, which is represented on our diagram alongside ๐ฎ. If we let ๐ฅ be the ๐ฅ-component of ๐ฏ and ๐ฆ be the ๐ฆ-component of ๐ฏ, then we can write these components like so. And you can think of these two numbers as giving instructions for how to get from the initial point to the terminal point of the vector.

You go ๐ฅ units right and then ๐ฆ units up. Letโs write this idea down. This is a similar idea to thinking of the coordinates of a point as being instructions which tell you how to get to the point from the origin. So what are the values of ๐ฅ and ๐ฆ?

Well we can basically read them off from the diagram by counting squares. ๐ฅ is two and ๐ฆ is five. To get from the initial point of ๐ฏ to the terminal point of ๐ฏ, we need to move two units right and then five units up. Our answer is therefore that the components of the vector ๐ฏ are two, five.