Lesson
U 8
2
ATB
form
Component
xz
xi
yz ya
A
go.io
I
3
4
S
7
ii
the vector that's
we call it
why
component form
7
7
r
Magnitude of
Y
r
a
Vector
r
Fix
OF_Magnitude
force
3
F
4
2
5
teh
47
49
49T
air
7TH
Unit Vectors
1 Vector
I
w
a magnitude
If
Z
You
by
can
v
of 1
and shouldn't care
unit vector
find this
dividing
some
scalar
bullshit you don't
a
non
Tabout
u
zero
scalartmultipleofabyit
magni
3
V
To find its magnitude
looks like this
take
which
both X and
square
together
y
To
X and
and
place
finish
y
separated
Don't
whole
I
T
4
y
add them
the
square root
thing
x
over
the
by
a
the
rationalize
original
make sure
no square roots
magnitude
comma
ng4y
out.to
forget
to
rationalize
pot
in
standard form
beebob
in the
are
that square
itself
ex
Sfg
over
over
root
irrational to
Ex
2nd
y ye
XZ
1st
X
Eye
1
It
goera
finding
12
magnitude
placing
it
and y
an
over
ordered
like
pair
this
1
T
the
is
u
vector
unit
Examples
4A
w
added
6
27
find magnitude
1st
gtfo
Imp
g
fy 6
Stine
2 fits into
lt
2
z into
I
3644T
40T
y
is
Beebob or
standardize
perfect
which fits 10
a
square
times
1
to
into
yet
canitnnafeusg.uaroemnoots
simplify further
zero
To
not done
To
I
7
I
magnitude
q
or
uf
backup
therefore
3
xt
x
f
Final
N
r
Linear
A different
vectors Cu
they
way
Vector
the
in
are
y
of representing
a
w
is
and
variables
I
three
y
Z
they
i
axis
j
are
written
competent
Lx y
x
X
y
if
equations
y
w
x
positive
as
note
magnitude of 7
unit
through linear
where
combinations
and j the
i is the
y
same
n
n
Combinations
E
0
t
answer
k
l
linear
combination
Same equation
Solving
form
Xz
get
the
X1
form
component
a
X1 y
S
3
example
equation
Xi
2
4
yz y
x
Xi
yr
4,5
E
D C 2,3
6,2
y
r
angle
I
ogetcomponent
r
n
Finding
Equation
t2j
Gi
tyj
r
and
y
e
Example
Xz
X
you
Xityj
equation
into
turn it
when
but
yz yt
component
as
Component form
and
O
NICOS
given
magnitude civil
WI Sin
o
o
cx.gs
y
i
H
n
ogelcomponent
m
O
wl
Use
magnitude
the
provided
and angle O
by
into
plugging them
the
these questions require
above
equation
calculator
a
Eixample
magnitude10
10x
IO
COS 120
4,7
10x COS
120
110
Sin
x
1207
ls
µ
X
angle1200
05420
IO
x
Sin
1207
plug into
calculator
8.667
t
answer
final
Finding
a
eat
Equations
tromformm
It
direction
angle
O
hin
Y
ex y
fmsi
n
Y
x
y
ComponentForm
tano
direction
angle
Liv
x
x
0
only things you need
magnitudeapand angleco
Cx y
b
eq
fang
fan
Vectors
of
0
direction
the
eg
Y
b
Itano
7
43
1
tan
O
tan
I
o
tan
CF
Quito
66
8070
Final Answer
Word Problem 7
We
looking for the
are
direction
angle Gano
f
order to
angle
or
tan 0
speed lui
and
In
si
we
get
need
the
to
direction
speed and
vectors for
develop
then combine
speeds
Ithrowing
both running
angle
direction
the
those vectors to get
tinged
1st
component form
151650 l 151 Sin 0
in
140
t
SMB
3rd
he's running forward
On the ground making
0 0
to
find
vector
2nd
for
throwing speed
125 0540,1251
sin
plug into calculator
and get 45,07
component
form
40
calc
4rth plug into
and get 219.15 16.067
add
Sth
together
5
0
219.15 16.06
L 24.15
find
speed
Iv magnitude
txt
16.067
o.fi onfano E
angle
an o
j
them
an.ie
16
062
s
Iv
I
333.60
O
I
full
minks
28.9
e
I
t
FinalAnswerse
Review
Lesson
2
form Lx
0 Component
Magnitude lol
0
Unit Vector
0
Keep
Xa
y
Vcx
Xi
Yz
yz
or
tG
u
in
mind
beebots
rationalize
Linear Combination
over
standardform
T
0
y
we
Yj
Xi
tip
ex
findcomponentformCx y
then change it to
a
linear combination
0
Form
Component
Finding
plug in
IV 1 Cos 0
Ivy Sin 0
given
wi and O
calculator
x
y
Finding Direction Angle
0
tan
component form
given
tano
2 hyos
given
o
E
IVI sin 0
Word Problems
for
0 Things to know
perfectly
question
the
understand
to write
of
lots
peace
have
U
8
Dot
3
Lesson
with
two
taft lb 12 142 represents
the
magnitudes
However
and Ibl
to find lat
b
a
products
Explanation
n
n
n
we
perpendicular vectors
a
la
µ
Teedtogetty
c
IbI
to
initial ordered pair
and
them
use
complicated
final
the
ike
this
by and
CayTreedt
to
and
get 14
irrelevant
the
of
part
for
to
but
equation
a
T
orthogonal
f
O
the vectors
be
Orthogonal
and
naif
perpindicular
are
and form
the
90 angle
IT
looks
betazbc
this
then
equal
shit
for
III
i
is
we
know
in
This
CIE 1917 6 22
since
Caz
the final
X
Example
U
zfy
V
8
z
1
S 4
V
U
tht 26
t
16
20
n.to
360
na
a
and Lv
CU
are
orthogonal
r
r
Using
r
Dot Product
magnitude
Relationship
to
r
find
l
u
4
142
thismeansindtkdotproduct
Of
vector
a
get
will
you
theme
if
and
magnitude
the
Example
Dot Product
SES
t
ZS
1512
142
Finding Angles Between
Vectors
Rule
can't
z
I al
144
5169
13
14
iz
12
t
a
_a
be
2
larger than
RX
1800Gt
radians
in
Cos 0
Equation
How to solve these
I
types
of
problems
Find the dot product of
7
b
and
by
doing
a
Find the magnitude
both
3
1
1
E
y
2
b
a
a
b
of
Ivl
vectors
Plug the
and solve
Example
a
s
into Cos 0
Dot product
b
1
1
divided
by product
magnitudes
of
Dot Product
T
nFtE
v.v
is
6 611 36
Magnitudes w
z
magnitudes
o
kebob
sta
al
y
q
2
full
luv 1
It2ft
i
i
a
3
Plug
into
050
1
of
the individual
vectors since
we need 14
not
and µ
40
361 4
900
2
18
6
24
not
b
1
3.1 Cos
O
Fro
05
Simplify
3 2
Cost
D
T.z.ro
t
3
4
is
Plug into
calculator
your
124.690
Answer
the
On TI 84 if
radians
gives you
change
z
q
cost
3 3
2
18
by
equation
pressing
to
or
degrees
DEDEDE
Vector
Projections
Proj
Equations
Step
1
Step
2
v
find
product
dot
the
magnitude ly
find
and
square
it
v
Ivi
Tty
Divide the dot product
Step 3
by
V
Step 4
of
Iv 12
magnitude
the
of
u
squared
IV12
should be
answer
this
Take
distribute it unto
an interger
which
looks like this
answer from
example
step
37
3
6
Example
of
3
9
F
product
Steeple dot
zG
u.v
Step
2
sum
magnitude IVF
by
SEE
cancel out
pµ
Divide dot
V magnitude
5
SO
Step 4
L
multiply to
TEETH
12
Ez
LE
WE
10
tribute
CE It
change signs
3,2
50
the
of w
it Wy in terms
3,27
solve
2
50
write
wz
t
Step 3
vectors
I
LI
3,27
U
57
wz
t
Tortoni
w
5
WE
m
Wy
U
10
1st
5
u v
Sk
t
ProjvU
one is
Findw z
I
E I
Tt
Ao
s
Cs
let
I
T E
Projuv
LI
Xample
2
PrgI
1
Dot product
z 4 t Gt3
8 t
2
Wet
10
18
Magnitude of
F
Wz
Wz
write
terms of
arm
wz
t
projuu
z
zZt
41
367
w
y u
K
in
and Wy
54 37 L E E
q2
3
Divide
b
T
40
Wz
dotproduct
magnitude
V
wz
by
V
FETT
signs
37 12
4
ft's
YI
Multiply
4
12
l
4
change
t
E
I
L9T
A
Final
A
e
A
7
Word Problem Example
this
For
Explanation
need to
problem
first find 2 things
we
The
7
showing
on
2
The
unit
After
we
pro
the car's
ramp
and
find
faff
vector
the
which
It
downward press
vector
case
this
in
represents
we
the
weight
its
w
find
is
the
these
ProjvF
V
ramp
2
This
jectiongnitudewin
I
the
keep
required
force
the
be
to
from rolling
car
down
F
F
3000 COS2700
IVI Cosa WI
since
3000 Sin 270
go
6,0
sooo
2700means straight
straight
down
z7o
Gf
down
ato
I
0
could've
that
You
deduced
sooo
was pushing
F
down
3000
from the origin o.O
2
Unitvector
this means lvl
Is
to
save
time
1
n3O
unit vectors
always have
qmagnideofy
3
l
nitV
catgulator
E
unit F
E
3
ProjuFf
I
Dot product
3 2
F
o
O
t
I
L
3000
Lo
3
v
Iz C
3000
1500
1,500
dot product
ylagnitudeotv72or1u12O.The
IVI
is
0
of
72 142
dotproduct
3.6
magnitude
500
unit
7
always
Therefore
a
1500
vector
150
2
q
3
ldotproductT
Multiply magnitude
8
T
A
1500
to
E
get Projuf
E
calculator
w
Distribute
75055
750
t
ProjvF
4
the
Find
of
X
Magnitude
Club
ProjvF
7502
750
Ialculator
to
trequiredtokeepy
the
car
1500
ereq_
from rolling
Ibsot
force
down
0
