FORMULARIO DE GEOMETRIA ANALITICA e ALGEBRA LINEAR new

Prévia do material em texto

CENTRO UNIVERSITÁRIO DE BARRA MANSA 
PRÓ-REITORIA ACADÊMICA 
CURSOS DE ENGENHARIA AFINS 
FORMULÁRIOS DE GEOMETRIA ANALÍTICA & ÁLGEBRA LINEAR 
PROFº M.Sc. CHEONG FAI TONG 
 
NOME: ______________________________________________ MATRÍCULA: _____________ 
PONTOS 
2
12
2
12
2
12 )()()( zzyyxxd −+−+−= 
 
RETAS ( IR2) 
r
PP
PP
=
2
1
 
r
rxx
x
+
+
=
1
21
 
r
ryyy
+
+
=
1
21
 
12
12
1
1
xx
yy
xx
yy
−
−
=
−
−
 
y = mx + n 
12
12)(
xx
yy
tgm
−
−
== α 
1
2
1
m
m −= 21
21
21
1
)( mm
mm
mm
tg >∴
+
−
=θ 
0=++ CByAx 0)()cos( =−+ dysenx ωω 
22
11
BA
CByAxd
+
±+
=
∓
 
 
VETORES ( IR3) 
kzzjyyixxPP
��� )()()( 12121221 −+−+−= 222 zyxv ++=
�
 vvv
���
⋅= 
v
v
u �
�
�
= 
),,(),,( 222111 zyxkzyx = 212121 zzyyxxvu ++=⋅
��
 θcosvuvu ���� =⋅ 
v
x
�=αcos 
v
y
�=βcos 
v
z
�=γcos 1coscoscos 222 =++ γβα 
v
vv
vu
uprojv
�
��
��
�
� 





⋅
⋅
= θsenvuvuAp
����
=×= pAA 2
1
=∆ ),,( wvuVp
���
= pt VV ⋅= 6
1
 
222
111
zyx
zyx
kji
vu
���
��
=× 
wuvu
wv
wvu ����
��
���
⋅⋅
=×× )( 
333
222
111
)(),,(
zyx
zyx
zyx
wvuwvu =×⋅=
������
 
 
RETAS ( IR3) 
vtAP �+= ),,(),,(),,,( 111 cbatzyxzyx += 










+










=










c
b
a
t
z
y
x
z
y
x
1
1
1
 
c
zz
b
yy
a
xx 111 −
=
−
=
−
 
 
PLANOS ( IR3) 
0=⋅ APn� 0),,(),,( 111 =−−−⋅ zzyyxxcba 0=+++ dczbyax 
 
CÔNICAS 
022 =++++ EDyCxByAx ( ) ( ) 222 Ryyxx cc =−+− 12
2
2
2
=+
b
y
a
x
 12
2
2
2
=+
a
y
b
x
 
a
c
e = 
12
2
2
2
=−
b
y
a
x
 12
2
2
2
=−
b
x
a
y
 xpy ⋅= 22 ( ) ( ) ),(;22 khVhxpky −⋅=− 
 
ÁLGEBRA LINEAR 
TACofAAdjAAdj
A
A )]([)()()det(
11
=∴⋅=− ji
ji
ji Aacof −−+ ⋅−= ,, )1()( 
∑ −−+ ⋅−⋅== jijiji AaAA ,, )1()det(