Video Transcript
Write π in component form.
The diagram shows vector π to be
drawn onto a grid. We are asked to write vector π in
component form. The component form of a vector is
typically written as π sub π₯ π’ plus π sub π¦ π£, where π sub π₯ is the
magnitude of the π₯-component of the vector and π sub π¦ is the magnitude of the
π¦-component of the vector. π’ and π£ represent unit vectors,
with π’ being in the direction of the horizontal axis and π£ being in the direction
of the vertical axis. Because weβre handwriting our
answers, we use a half arrow over the letter π to represent that itβs a vector. In text form, we bolded it. In the π’ and π£, we see little
hats to represent that theyβre unit vectors. In text form, these can also be
bolded.
To find the component form of
vector π, we need to determine how much of vector π is in the horizontal direction
and how much of vector π is in the vertical direction. Looking at the grid, we can see
that vector π is one, two, three units to the left of our screen. This is considered negative
three. We could then say that the
π’-component of our vector has a magnitude of negative three. Looking back at the grid, we can
see that the π¦-component or the vertical direction has a magnitude of one, two
units pointing towards the top of the screen, which would be a positive two. We could, therefore, say that the
π£-component of our vector has a magnitude of two. Based on the diagram, the component
form of vector π is equal to negative three π’ plus two π£.
