Video Transcript
Consider the vector in the
diagram. What are the coordinates of the
terminal point? What are the coordinates of the
initial point? And what are the components of the
vector?
For the first part of the question,
we recall that when a vector is represented in a coordinate plane, the terminal
point is the point at the end of the line segment in the direction of the arrow. We can think of this as where the
vector is pointing. And from the diagram, we see that
this has coordinates negative seven, negative one.
Similarly, for the second part, the
initial point is the point from which the line segment starts, the arrow being
directed away from it. From the diagram, we see that this
has coordinates negative one, positive two.
For the final part, we’re asked to
find the components of the vector. And for this, we recall that the
components of a vector from an initial point 𝐴 with coordinates 𝑥 one, 𝑦 one to
terminal point 𝐵 with coordinates 𝑥 two, 𝑦 two are the differences between the
𝑥- and 𝑦-coordinates, respectively.
In our case then, the 𝑥-component
or the horizontal component 𝑎 is equal to negative seven minus negative one. That’s the difference between the
two 𝑥-components, terminal 𝑥 minus initial 𝑥, and that’s negative six. Similarly, for the 𝑦- or vertical
component, we have negative one minus two. That’s the difference between the
terminal and initial 𝑦-values, and that’s equal to negative three. Hence, the components of the given
vector are negative six and negative three. And hence, the terminal point of
the given vector is negative seven, negative one. The initial point is negative one,
two. And the components of the vector
are negative six and negative three.
