3D
Vector
Vector Quantities
-
P
( x.
I
L
=
EX
y
l
)
z
,
O
,
.
o
>
ATB
:
r
=
( zi
f
=
-
>
I
=
=
I
+
-
Vertu
+
3
2
,
-
o
,
,
I
g)
( 3k
t
-
z
>
C
i. a. is
( 2 -1,33
=
,
=
of
3D
(
3
.
I
is
.
Vectors
-
IT
-
A
A. B
coordinates
=
O
→
ITI
-
tal
-
=
tri
ijtzk
-
-
-
JEFE
$¥¥aI#
I
yT-_
YZ
XZ
-
t
c-
-
I
=
ZZ
¥z#
(
xityjtzti )
I
151=56
I
=
1¥
=
,
-
Fg
L
-
ti
properties
:
an
I
=
a. it
azj
=
b.
by
it
task
tbsk
-
jerk )
f- ¥ I. E )
-
.
-
,
>
B
k)
y
,
)
of
III
,
=
(y
'
ans
-
¥
¥
.
EX F
..
N
in
To
=
A =L
Length
yjtzk
< a , .az
^
V
-
,
I
,
(x
=
JTTt.BIZ
=
xi
Unie
=
)
1,03
,
xixyjtzk
=
off
surface
at
top
T
l
O
-
i
-
-
(
=
JB
-
Displacement
.
.
>
OF
-
/
Anagni nude
-
j
JB
=
=
T
=
,
Velocity
:
Atb
-
if
Equal
a.
-
b
,
Law
aa
,
atb
Catb
Eto
Vector
-
It
C
-
-
-
-
Distributive
MER
KI
Parallel
E
Director
Cosines
-
-
mail
at
t
na)
Oj
-
-
-
t
J
EX
of
-
+
=
=
a.
i
it a
+
Lo
=
copy
Iga
mcatb)
0,0
)
man tmb
-
cos
,
A
=
.
task
jerk
,
151=0
.
T
1¥
Z
Li 1,52 >
,
KER
,
ok
x
-
costs
for
coff
-
Cbtc )
KJ
¥¥
t
mask
c-
b,
-
as
.
may
i
-
KER
,
2
cost
( as tb 3) h
t
ta
-
Oi
Itc
=
bz
I
-
Addie 're Inverse
Law
-
-
b
-
↳
-
)j
-
man
R
Law
Commutative
Zero
-
( as tbz
t
-
ME
Associate
-
i
-
Multiply
-
b. I
t
,
b
a-
-
(a
=
-
-
-
-
ooh
-
( ¥)
'
,
¥,
-
2
a
aslant
I
III
=
2
,
of X
a
-
I
=p
=
}
cos
=
,
,
y
cosy
=
=
-£
n
~
-
Doe
produce
a
a
properties
i i
:
-
T.ci
30
m
ER
.
a.
n
k k
-
a.
b
a.
b
b
=
-
-
-
-
ma
,
a
b
(
m
-
a.
I
( at b )
-
C
O
⇐s
=
faith
=
( a. tb )
,
,
,
T
-
-
b
C
-
perpendicular
⇐>
=
are
A, C,
b
t
bz
,
aztbz >
( cc : tczjtcsk )
i
,
C
(
-
cc
.
C-
i
Cs
( aztbz )j (
t
)
C
,
Itczj
t
( Ciieczjtcsk )
t.az tbs ) h
=
181151
b)
L
EX
-
ta c
et
-
=
asbs
t
if
only
o
b
a.
=
=
-
coso
t
,
Az Cz
t
b
z
Cz
t
Az Cs
t
b z Cz
11
a
EX
:
an
-
Ctb
( 1,2
=
III
oso
=
Ty
=
C
-
,
A , C,
=
-3
b
a
o
-
-
and
azbz
t
scalar
=
-
I
'
-
-
c
-
crib ,
=
Cbtc )
atb )
(
|
b
-
tall blast
-
jj
-
-
b
-
a
I
t
Az Ca
(
2,5
)
,
,
151--533
=
o
-
,
cos
t
Az Cz
-25
"
(
-
n
)
t
b
,
C,
tbzcz
t
bsc]
Csk )
-
of position
Ruler
i
ATI
.
Z
.
5- an
-
-
OTP
nn5
=
nth
EX
a
( 1.2.33
=
JE
b
,
=L
-
4. b. 8)
A
B
,
b
=
o
E
Scalar
-
vector
7
Resolute
scalar
(
comp , Ca )
I
=
I
EX
(
v
a
I
=
T
-
-
¥3
Comfy
b
151
41,2
=
component )
#
I
-
.
(
Ca )
-
37
2,5
=
,
I
b
,
-
z
-
-
f
z
,
5
-
,
z
)
151=533
,
>
I
=
¥
=
#
s
1.2
,
-3
>
C 2.5
.
-
,
z
>
www.wee
Phys
ca)
=
-
-
compbca ) B
ta 5) I
-
18
comps Las
=
Es
=
€515
b
-
pwjbca )
b
=
=
=
comps
cast
¥ ( ¥12.5
(
2
,
5
,
-
resolve
,
2)
-
z>
)
-
Linear
n
Dependence
rectors
{ Vi
,
Va
a
,
Independence
and
)
Va
.
.
LD
are
Ri
It
{ ijiy
{jk)
,
Iki :3
.
LD
not
A
R, V ,
.
t
R
z
Vz
not
'
Ott
-
an
iii.
C
T
O
-
JBL
(
=
of
(I
'
=
a
=
=
=
I
'
I
-
-
b
O
b
I
OTI
-
t
)
-
-
(I
-
COI
-
'
-
b b
'
)
-15 )
a. a
lap
)
-
b
-
a
all zeros
t cut
B
Assume
AE
,
LID
so
.
Rai edu
-
.
±
.
.
An Vn =D