### Video Transcript

Weβve got π΄π΅; itβs the vector
three π plus four π. ππ is the vector negative two π
plus three π. And weβve just got to add those two
vectors together.

So the first stage is just to take
vector π΄π΅ and add vector ππ. And all we have to do is add the
πs together first, and then add the πs together second. So three π add negative two π is
just one π, so thatβs π. And four π add positive three π
is seven π. So thereβs our answer, π plus
seven π. Simple as that, add the
π-components together, add the π-components together, look out for the negative
signs and- when youβre doing those calculations; but otherwise, thatβs a pretty
straightforward process.

So letβs just visualise that
example. So we had three π plus four
π. So weβll be going positive three π
and then positive four π, this is the ππ vector. So there we are. Weβve just laid that down at the
origin. We couldβve laid it anywhere on
the-on the graph. Now adding vectors, we just lay
them end-to-end. So what we were adding, π₯π¦, was
negative two π plus three π. So weβre effectually starting π₯
from π΅, so π₯ lays on top of π΅ and weβre going negative two π. So weβre going two in the negative
π₯-direction and weβre going positive three π, up to here.

So adding vectors is just a matter
of laying them end-to-end on the graph. So we laid π΄π΅ down, which started
here and ended here, and then we just added ππ to the end of that, laid that onto
the end. So that started from where we just
finished off and then ended up here. So the resultant vector is this
green one here. And to get from the beginning of
the green vector to the end of the green vector, we had to go positive one in the
π₯-direction. So thatβs one π, or just π. And in the π¦-direction, weβre
going up seven all the way up here. So thatβs plus seven π.

So when youβre doing these
questions, it really is just a matter of adding the π₯-components together, adding
the π¦-components together, and coming up with a simple answer. You donβt need to do all this
graphical checking. But Iβm just hoping that thatβs
giving you some extra insight into the process and why it works.