### Video Transcript

Consider the vector in the given
diagram. What are the coordinates of its
terminal point? What are the coordinates of its
initial point? What are the components of the
vector?

We say that a vector has an initial
point, that’s where it starts, and a terminal point, that’s where it ends. So to find the coordinates of the
terminal point of the vector in our diagram, that’s the vector 𝐯, we need to find
the point at which the line segment that represents that vector ends. Remember, the arrow represents the
direction of the vector. So in this case, we move from left
to right. This means the vector ends
here. We can therefore say its terminal
point has coordinates at two, one.

Next, we’re looking to find the
coordinates of its initial point. And remember, we said that that’s
the start of the line segment. That’s here. The coordinates of this point are
negative one, three. So that’s the coordinates of the
initial point of our vector.

The third and final part of this
question asks us to find the components of the vector. We split two-dimensional vectors
into components that represent the horizontal and vertical motion separately. In order to see what these are,
we’re going to add a right-angled triangle onto our vector 𝐯. This will split it into its
horizontal and vertical components. The right-angled triangle we add is
as shown.

Let’s look at the motion in the
horizontal direction. We start at 𝑥 equals negative one,
and we move one, two, three spaces to the right. Next, we consider the vertical
motion. We start at a 𝑦-coordinate of
three, and we move one, two units down. We can therefore write the vector
𝐯 as shown. We can use a column or these angled
brackets. And the vector is three, negative
two.