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Tieát 25 
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Hoạt động của GV và HS Nội dung bài học
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Hoạt động của GV và HS Nội dung bài học
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D (EF'5-D39(G(-
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AJ4$78-
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#-78#$&1(G(-
1!9#&ExE&G(XR@1-
:'#("0;&
:'<.6"=!)!8>?#@3A#B&:=E5(%.F./K(0-
:'#@3"0C3#B&
AP(4$78-
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Hoạt động của GV và HS Nội dung bài học
Q!7>"&18
AR?7>"&18
!7>"&1 83
(4$7
""L&MM,A7!'70M"0C - !C - C - NO:OP - %QR - 8C - !%QR'"3 Trang 8

l
, , , ,
6 2 6 2 62      + + =− − −
, , ,
, , , ]      + + + + + + =
AQX*Ee"*&G(-
Q,qG((4$78
AR?PEG((4$78-
AQX7>"&1 83-
AR?QX*
AQX
|>t2`;}!;m6&1k`
&|>D2`;}`;!6&1k
m
|>t2},;!;}`6&1k
!z

|>t22m;}`;{6"&1k,
|
, , ,
6 2 6 2 6 ~2 ` z !  + + =− − +
>t2`;z;}!61k`
&|
, , ,
s , !s ,s ]     + + − + − − =
>t2`;}!;•6
1
, , ,
2 !6 • ,s !]` + − + + ==
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, , ,
, , •, z !, !]] ]     + + + − − − =
, , ,
z , s m] ]     + + +⇔ − − − =
>t2},;!;`6
1
, , ,
! ` m] •2 ,6 + + + == −
|
, , ,
• , ! ]    + + − − + =
#|
, , ,
` ` s` • !m ` ]     + + − + + − =
,qG((4$784e
9(
|D34e1o"5o2z;}`;{6"2,;!;`6

>tE% o
⇒
t2`;}!;m6
1tok
, , ,
2 ,6 ,! `+ − + =
?G(4$78E
, , ,
6 2 6 2 6 ~2 ` ! m  + + =− + −
&|bC%o2m;},;!6"3>D2`;}`;!6
1oDk
, ,
2 !6, m+ − =
?G(4$78E
, , ,
6 2 6 2 6 m2 ` ` !  + + =− + −
|>t2},;!;}`6"&EUt
1Utk
, , ,
2 !62 ,6 ` !z+ − + =−
?G(4$78E
, , ,
6 2 6 2 62 , ! ` !z  + + =+ − −
|D3>t22m;}`;{6"&1k,
?G(4$78E
, , ,
6 2 6 2 62 m ` { z  + + =− + −
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A?(4$78>t&1
:'OEAb1!9#"c1!&

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Ab/"5&p(#V#&€J4$78(W•
O'd"?##B3&
A

AJ4$((

AXr0KL&=
""L&MM,A7!'70M"0C - !C - C - NO:OP - %QR - 8C - !%QR'"3 Trang 9

,`|!,|,]!`},•|!,|,]!` !~
Tiết 30 jr
 !"#$%&
'#(")!&
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(4$7:C 8(WB"38.. ,8
(W'1*j!%!8(W-
'*+&
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"(4$7:C 8(W"149*j!%
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D (EF'5-D39(G(-
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AJ4$7:C 8(W-
,'%456&
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AQX'OEPC8(W"#$n(4$"#$(( 8

(W-
:'#("0;&
:'<.6"=!)!8>?#@3A#B&:=E5(%-
:'#@3"0C3#B&
AD
2 ; ; 6; 2 ; ; 6; 2 ; ; 6; 2 ; ; 6
           
               
! , , ! , ` ! , `
2 ; ; 6; 2 ; ; 6; 2 ; ; 6           = = =
r
r r
P'
:',D>#3E#&
Hoạt động của GV và HS Nội dung
Q!
AR? Nhắc lại khái niệm vectơ pháp
tuyến của đường thẳng, vectơ chỉ phương
của đường thẳng đã học.
- HS: Vectơ pháp tuyến là vectơ
0≠
r
vuông góc với đường thẳng đó.
Vectơ chỉ phương là vectơ
0≠
r
nằm trên
đường thẳng song song hoặc trùng với
đường thẳng đó
Q,

AR?5'113
45"7-
AR?(0*?l!
AQXi*"4C*-
t-?#$(( 8(W
b=FVectơ
r
n

0≠
r
được gọi là vectơ pháp
tuyến của mặt phẳng
( )
α
nếu đường thẳng chứa
vectơ
r
n
vuông góc với mp
( )
α
(gọi tắt là vectơ
r
n
vuông góc với mp
( )
α
)
Kí hiệu:

r
n
⊥
mp
( )
α
vDMx
 
r
n
E vect$((L!8(W7
r
kn
cOE?J 8(W3-
trong hệ tọa độ Oxyz nếu
a
r
= (a
1
, a
2
, a
3
),
b
r
= (b
1
, b
2

, b
3
) là hai vectơ không cùng phương và
các đường thẳng chứa chúng song song hoặc nw
trong một mp
( )
α
thì vectơ
n
r
=
a,b
 
 
r r
=
2 3 3 1 1 2
2 3 3 1 1 2
a a a a a a
, ,
b b b b b b
 
 
 
 
là một vectơ (p
tuycủa mp
( )
α
.

""L&MM,A7!'70M"0C - !C - C - NO:OP - %QR - 8C - !%QR'"3 Trang 10

|
‚  ƒ 
r
r
k2},z;}!,;}!,6
&|
‚  ƒ 
r
r
k2,z;!`;,{6
AR?GV).r.EG-
AR?u(0i?l,-
AQXi*"4C*-
2,;!; ,6 = −
uuur
2 !,;s;]6 = −
uuur
 ƒ‚ 2!,;,z;,z6  = =
uuur uuur
r
Q`
AR?.".F"B,
&
AR?5(4$7:C
 8(W-
AQX#„)(-
AR?PEG((C 8(W
AQX7!%"!"#$((

 8(W
Qz
AR?(0=F(4$7
8(W-i?l`?lz-
AQXi*"10-
AR?GV).r.-
Qm
AR?V)4e9(8&
lk]
!`./oD&w]
``./oDk]
j378(W
AQX#„)(-
AQX(0i*?lm-
Khi đó cặp vectơ
a
r
,
b
r
được gọi là cặp vectơ chỉ
phương của mp
( )
α
.
?10!1
‚  ƒ 
r
r
&

|

r
k2`;];}s6

r
k2,;}z;]6
&|

r
k2!;}s;,6

r
k2z;`;}m6
R*
|
‚  ƒ 
r
r
k2},z;}!,;}!,6
&|
‚  ƒ 
r
r
k2,z;!`;,{6
?10,UVY`%o2,;}
!;`62z;];!6D2}!];m;`6-7!"#$
(( 2oD6
2,;!; ,6 = −
uuur

2 !,;s;]6 = −
uuur
 ƒ‚ 2!,;,z;,z6  = =
uuur uuur
r
tt-J4$7:C 8(W
!-b=F(4$7:C 8(W
E(4$73oVDYlk]"5
oDKe&w]2
, , ,
]  + + ≠
6
GV)
2
α
63(4$7:CEoV
DYlk]7?J

r
k2o;;D6
2
α
6C%
] ] ] ]
2 ; ; 6   
"G

r
k2o;;
D6

]
r
E?J3(4$7:CE
] ] ]
6 6 6 ]2 2 2        + + =− − −

?10`Q[7!?J 8(WzV},}
sY{k]


r
k2z;},;}s6
?1 0z qG( (4$7 : C8(W
2gJ6"5g2!;!;!62z;`;,6J2m;,;!6
2`;,;!6" =
uuuur
2z;!;]6# =
uuur
 ƒ‚ 2 !;z; m6" # = = − −
uuuur uuur
r
?G(4$7:C2gJ63
!2 z6 z2 `6 m2 ,6 ]
z m , ]
  
  
− − + − − − =
⇔ − + − + =
,-D4e9(P
      UVY    8  (W  2

α
6  3
(4$7oVDYlk]
|lk]
2 6
α
⇒
C/U3(oV
DYk]
&|ok]
2 6
α
⇒
..8'0UV3
(DYlk]
k]
2 6
α
⇒
..8'0U3(
oVDYlk]
Dk]
2 6
α
⇒
..8'0UY3(
""L&MM,A7!'70M"0C - !C - C - NO:OP - %QR - 8C - !%QR'"3 Trang 11

oVlk]
|okk]

2 6
α
⇒
..8L2UV63
(DYlk]
kDk]
2 6
α
⇒
..8L2UY63
(oVlk]
okDk]
2 6
α
⇒
..8L2UVY63
(lk]
vGV)g8(WC`%o2;];]62];
&;  ]6  D2];  ];  6  3  (4$  7
! ]
  

  
+ + = ≠
2( (#T6
?10m`%g2,;];]6
2];}!;]6J2];];`6-?(8(W2gJ6
3
! s ` , s ]
, ! `

  
  + + = ⇔ − + − + =
−
:':2%^#_5>#"`L!K!a&
AP?J 8(W-
AP(4$7:C 8(W-
AP"(C 8(W-
:'OEAb1!9#"c1!&
Ab/"5&pT49'"
Ab/"5&p(#V#&€J4$78(W•
O'd"?##B3&
A

AJ4$((

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Tieát 31 jrU""S
 !"#$%&
'#(")!&
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(4$7:C 8(WB"38.. ,8
(W'1*j!%!8(W-
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AQX'OEPC8(W"#$n(4$"#$(( 8
(W-
:'#("0;&
:'<.6"=!)!8>?#@3A#B&:=E5(%-
:'#@3"0C3#B&
AP(4$7:C 8(W
:',D>#3E#&
Hoạt động của GV và HS Nội dung
Q!
AR?45^*1-
AQX#„)(-
Q,
AR?4"10!,(0-
AQXEP&*E&#%& 
7
AQX(0"=14$/ ,8
(W-
Q` /EG((4$
7:C 8(W-
AR?4"10`zm-
AQX*
ttt-?=14$/ ,8(W
D8(W

2 6
α

! ! ! !
]      + + + =
2 6
β

, , , ,
]      + + + =
vQ!
2 6
α
T
2 6
β
`
! !
, , `

 
  
≠⇔ ≠
vQ,
2 6
α
||
2 6
β
`

! ! !
, , ` ,

  
   
= ≠⇔ =
vQ`
2 6
α
L
2 6
β
`
! ! !
, , ` ,

  
   
= =⇔ =
vQz
2 6
α
⊥
2 6
β
! ,
! , ! , ! ,
]
 
     

⇔ ⊥
⇔ + + =
r r
?10!<)"=14$/ 8(8(W
6
! !
6 2 , ` z ] 2 6 m ~ ]     
α β
+ + + = + − − =
&6
, ,
6 2 m ] 2 6 , , , !] ]     
α β
+ + + = + + + =
6
` `
6 2 , ` ! ] 2 6` s ~ ` ]     
α β
+ + + = + + + =
R*
6
!
6
! , `
2
! m !
α
≠ ≠ ⇒
−
T

!
62
β
&6
, ,
6 | | 6
! ! ! m
2 2
, , , s
α β
= = ≠ ⇒
6
` `
6 6
! , ` !
2 2
` s ~ `
α β
≡= = = ⇒
?10,7%8(8(W."3
6  ,2 , ~ ] 2 6s !] ] $ $   
α β
+ + − = − − − =
3
2,; ;, 6 $ $
α
=
r
2s; !; !6
β

= − −
r
62 2 6 ,-s 2 !6 2 ~6-2 !]6 ] z$ $
α β
⊥ ⇔ + − + − − = ⇔ =
?10`?(4$78(WC`%
o2}!;,;`62,;}z;`6D2z;m;s6
2`; s;]6
2m;`;`6


= −
=
uuur
uuur
 2!•; ~;`~6 
 
 
= −
uuur uuur
?J 8(W
2 !•; ~;`~6 = − −
r
?G(4$78(W7E
""L&MM,A7!'70M"0C - !C - C - NO:OP - %QR - 8C - !%QR'"3 Trang 13

!•2 !6 ~2 ,6 `~2 `6 ]
!• ~ `~ !]{ ]
  
  

− + − − + − =
⇔ − − + − =
?10z?(4$7
2 6
α
C,%o2`;!;
}!6  2,;  }!;  z6  "  "  3  8  (W
, ` { ]  − + + =
2 !; ,;m6 = − −
uuur
;
2,; !;`6
$
 = −
r
 2 !;!`;m6
$
 
 
 
= −
uuur
r
?J 
2 6
α
E
2 !;!`;m6 = −
r
?G(C8(WE

!2 `6 !`2 !6 m2 !6 ]
!` m m ]
  
  
− − + − + + =
⇔ − + + − =
?10m?(C8(WC%g2!;},;`6
"..8(W2J6
, ` z , ]  + − − =
2 6
α
..2J6P
2 6
α
3?J
2,;`; z6 = −
r
?G(C
2 6
α
E
,2 !6 `2 ,6 z2 `6 ]
, ` z !s ]
  
  
− + + − − =
⇔ + − + =
:':2%^#_5>#"`L!K!a&
AP"(C 8(W-
APV)"=14$/ ,8(W-

:'OEAb1!9#"c1!&
Ab/"5&pT49'"
Ab/"5&p(#V#&€J4$78(W•(IE
O'd"?##B3&
A

AJ4$((

AXr0KL&=
]s|]!|,]!z}!!|]!|,]!z ,!
Tieát 32 jrU""S
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Hoạt động của GV và HS Nội dung
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Hoạt động của GV và HS Nội dung

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2 !;];,6
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""L&MM,A7!'70M"0C - !C - C - NO:OP - %QR - 8C - !%QR'"3 Trang 19
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AR?
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2 6

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Hoạt động của GV và HS Nội dung
Qz

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