Coordinate
systems
vectors
Vector
processes
addition
subtraction
dot
cross
Coordintesystem
A Three
used
in
this
class
Spherical
Cylindrical
iii
ix
O
y.z
02190.2
it
As
you
might expect
cartesian
L
is
Ir
0.0
T
good for box
shapes
cylindrical for cylinder shapes and spherical for spherical
shapes
Conversion
to
from
Cartesian
cylindrical
cylindrical
Cartesian
X
p
y
f
Z
spherical
0
co
cartesian
sing
r
0
z
Vectors
are
Tay
it
are
Fexample
0
cos
or
spherical
Spherical
F
xtytz
r
É
arata
0
arctan
o
and
quantities defined by a single sit
de
For example
temperate mass volume
both may
velocity and force
quantities
with
will need both in this class
and life
We
sin 0
Scalars
Scalars
Vectors
of
cylindric l
Cylindrical
f
si
r
to
sing
050
Z
Conversion from
spherical
ft
it de
re
and direction
classes
our
careers
A Simple example
I
It
magnitude
vz I
Vy y
vitri
up
IT
I
where
direction
Y E
but
Any vector
are
u
be
unit
a
by its magnitude
we
If
this
can
put
its
located
at
the
with
by jest dividing
vector
E
F
at
vector
vectors
of unity
magnitude
a
can
vectors
it
is
any place
origin
we
ha
want
we
e
T
or
T
mags
Taiz
some
ya
z
L
We
can
have
vectors
in
other
c
Cylindrical
F
Ve
ft f I
Viz
T
ordinate systems too
Spherical
K it Ve
is
YE
VectorOperation
I
f It Fy y tf É
Scalar multiplication
Addition Subtraction
n
I
I
A
I
I
c
g I
g
f I
c
j
gyY gzÉ
f Ig
fy y
c
X
Fy Ig
I
B
D
fzÉ
Fz g E
A
B
c
t
I
B
I
R s
t
t
B
I
a
J
Dot
Product
t
I g
fig
fy gy
t
III Igt
B
I
B
A
A I
A
B
A I
A
F B
A B
B
tf
z
angle between
cos
cos
g
vectors
1900
cos
1800
cos
o
0
A B
A
B
A B
angle between
Tal
Ix 5
Gross product
vectors
f
5
sin
D a
ector in
normal unit
what does normal
Ah
It's
5
out
by
But
there
both
know
we
The
cross
the
right
the
product
hand rule
b plane
a
unit
of
the
the
I
in
which
mean
vector
pointing
2D
plane made
I
and
directions
down
and
up
How do
two
are
in
vector
unit
the
it
vectors
could point
above
case
way
x
follows
3
Point
index finger
your
the first
vector
along
and your second
the
will
finger any
second vector
point
in
the
direction
a
The
normal
vector
direction of your thumb
b plane
A
I
B
Axis
if
T
I
A
J
BxA
B
points into the page
9
I
9
Axis
0
J05xApoi.ts
out
of the page
J
Notile
a
T
A xD
Bx
B
Axis
A B
sin
A xD
A B
sin
180
A xD
A B
sin
Oo
B
t
i
190
n
the page
A Bi
0
A
5
few examples
using
A
5 5
Y
x
I
2
z
Y É
Z XY
Z
X
X
Cartesian
x
X
y
Z
p
Y
0
coordinates
q
Ey
But what
if
you
I
I
9
5
complicated
have
a
b I
use
the
determinant
a
5
5
bay
It's just
a
5
9263
4
Y
E
a
an
as
Ok
in
É
to
help called
b
b
NOTICE
4
azbz
I
b
thinking what the hell is that
symbol to do an operation
3
1
I
a
t
I
b
You might be
as É
Y
matrix technique
we
vectors
a
that
vector
by azb
E
E
e
it
a
E
I
e1
should
cross
be
enough
products
azb
bz
I
He
of
a
crash
course