Formulário Geometria

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22|| bav
0
1
||
)(sen
v
b
||
)(cos
v
a
a
b
)(tg
30° 45° 60°
2
1
2
2
2
3
2
3
2
2
2
1
3
3
1 3
v v 0v 0 R
ACvu ACBCAB
ACvu ACADAB
vuvu )(
DBvu DBCBDC
u v vu
vu
v nvvv ,...,, 21 v
nvvv ,...,, 21
nnvvvv 2211 Rn,...,, 21
R2 R3
R2
jyixv ),( yxv
AB ),( AA yxA ),( BB yxB
22 )()(|| ABAB yyxxAB
AB
AB
xx
yy
)(tg
AB OAOBAB
21 ... vkvkvk ),( 21 vvv Rk
2121. yyxxvu jyixu 11 jyixv 22
cos.||.||. vuvu 1800
R3
kzjyixv ),,( zyxv
222|| zyxv
AB 222 )()()(|| ABABAB zzyyxxAB ),,( AAA zyxA
),,( BBB zyxB
321 .... vkvkvkvk ),,( 321 vvvv Rk
212121. zzyyxxvu kzjyixu 111 kzjyixv 222
cos.||.||. vuvu u v 1800
),,( 321 aaaa ),,( 321 bbbb
kbabajbabaibaba
bbb
aaa
kji
ba )()()( 122131132332
321
321
Rn
),...,,( 2211 nn vuvuvuvu ),...,,( 21 nuuuu ),...,,( 21 nvvvv
),...,,( 2211 nn vuvuvuvu ),...,,( 21 nuuuu ),...,,( 21 nvvvv
nvkvkvkvk .... 21 ),...,,( 21 nvvvv Rk
nn vuvuvuvu .... 2211 ),...,,( 21 nuuuu ),...,,( 21 nvvvv
baxy a b
).( 00 xxmyy
AB
AB
xx
yy
m ) ,() ,( 00 AA yxyx
) ,() ,( 00 BB yxyx
0cbyax
)direçãovetor ()posiçãovetor ()( ttr Rt
R2 ),.(),()( BBAA yxtyxtr
R3 ),,.(),,()( BBBAAA zyxtzyxtr
R2
BA
BA
ytyy
xtxx
.
.
R3
BA
BA
BA
ztzz
ytyy
xtxx
.
.
.
||.||
|.|
cos
vu
vu
2
0
0. 2121 vvrr 1v 2v 1r 2r
1r 2r 1r 2r
0
r1 r2 P
0dczbyax a b c n
000 czbyaxd 0.APn PA,
vtutAP 21 u v PA, Rtt 21,
22110
22110
22110
ctctzz
btbtyy
atatxx
123312231213132321
333
222
111
).( zyxzyxzyxzyxzyxzyx
zyx
zyx
zyx
wvu
) , ,( 111 zyxu ) , ,( 222 zyxv ) , ,( 333 zyxw
21
21
.
.
)cos(
nn
nn
900
R2 22 )()(||),( ABABBA yyxxABd
R3 222),( )()()(|| ABABABBA zzyyxxABd
||
||
),( u
vu
d rP
22
00
ba
cbyax
d rP
||
),( P=(x0, y0) r: ax+by+c=0
222
000
cba
dczbyax
d P
||
),( P=(x0, y0, z0) : ax+by+cz+d=0
22
0
2
0 Ryyxx )()(
1
)()(
2
2
0
2
2
0
b
yy
a
xx
1
)()(
2
2
0
2
2
0
b
yy
a
xx
1
)()(
2
2
0
2
2
0
b
yy
a
xx
cbxaxy 2
x
a
acbb
x
2
42
y (0, c)
a
acb
a
b
V
4
4
 ,
2
2
cbyayx 2
x
a
acbb
y
2
42
y (0, c)
a
b
a
acb
V
2
 ,
4
42