Hey guys this is Eddie the Magic Monk. Welcome to another vectors tutorial
today we're gonna show you guys how to do some basic vector operations in
geogebra so the first thing I want you to do is open up a new window in
geogebra by doing file new window and then what I
want you guys to do is to right-click somewhere on your Cartesian plane and
then you're gonna click on graphics and what I want you to do is set the
dimensions of what you can see to about negative 10 on the x-axis to 10 on the
x-axis and then negative 10 for the y-axis to positive 10 okay and then for
the grid I want to show the grid and I want a distance of 1 for X and 1 for y
okay so and then if you turn this off you should be able to see that it's all
working ok so now what I want you to do is go to options point capturing and
choose snap to grid and then the reason for doing that is because now when we
draw a vector so if you choose this line through two points click the down arrow
and choose vector between two points now when we select the origin and now you
can see that it snaps to the grid a little bit easier now that we've turned
on snap to a grid so let's select the point two five so you can see that the
first vector we can drag it around and let's go to two five okay let's do a
second vector from zero to four negative two
okay so I have two vectors all right the first one let's show the label so
right click on that and show label so that's vector u and then this one is
show label that's vector V okay so let's do the first operation which is V minus
u so if you remember when you subtract when you do a subtraction with vectors
it gives you the vector if you do V minus u it gives you the vector of a
vector going from the head of U to the head of V so for example if you did
vector W equals V minus u you end up with the vector W which is the vector
this vector here is the same as the vector going from point B to Point C so
vector u to the head of vector V so if you want to verify that okay you can
simply use the vector between two points tool and go to vector from point and if
you click point B and then if you click vector W okay you end up with an
another vector here which is vector Z which is the same as vector W okay
because you can see they have exact same coordinates okay so that means W is V
minus u okay so let's change it up a little bit
and let's try the U + V okay so what I want to do is get rid of these two
vectors so now because we're doing u plus V I want to create the same vector
here at the end of vector U at the head of vector u I'm gonna create I'm gonna
move the vector V to this position so what I do is I choose vector from point
click this point here click vector V so I've created a vector here that's
identical to vector V so you can say vector V is over here and what I'm going
to do is create another vector so I can delete vector W because oh no that's
vector W over here so I'm going to do vector Z is equal to u plus V okay and
you can see here vector Z which is equal to u plus V is the same starting from
the origin go to vector U which is you know we end up here and then vector V so
we end up here so u plus V is Z so this again proves to you vector addition and
subtraction okay so let's do vector multiplication so as you know here we
have vector u so if we create another vector let's call it vector X actually
vector a and let's make vector a equal to three times U and you can see here we
have a vector called vector a so this is vector a
and we can show the label so Vector a right now is three times the length of
u okay so you can also do vector B is equal to three times
u three times u so that's what we have here vector a really but we're
using vector u so I can show you a combination of scalar multiplication and
let's say we want to add this vector here which is vector V so three u plus V
3 u plus V and we end up with this vector so where does this come from well
if this vector is 3 u and from here to here is vector V so I'm just gonna prove
to you that it is so I'm gonna go vector from point and I will click this and I
will click this oops I should create a point over here first so create a point
over here and then I go vector from point click this point click this
vector so you can see it see here this vector which I have is vector B is equal
to 3 u plus V and it is because we have three u over here and we have V over
here so this vector is 3 u plus V okay thanks for watching guys see you next
time.