【2019年整理】《步步高学案导学设计》-2014学年高中数学苏教版必修4【备课资源】第2章232平面向量的坐标运_图文
2.3.2
2.3.2 ()
1
2
3
1
""
2"" x1y2 x2y10 ab a b x1y2 x2y10.
2.3.2
1
a(x1y1)b(x2y2)
(1) ab x1y2x2y10 .
(2) ab x2y20 xx12yy12
.
2.3.2
2P1PPP2 PP1P2
(0) P P1P2
1 P P1P2
(1) P P1P2
(1,0) P P1P2 .
2.3.2
a b
ab.
2.3.2
1 a(x1y1)b(x2y2)(b0) ab
x1y2x2y10
a(x1y1)b(x2y2)b0.
x2y2 0 x20.
ab ab (x1y1)(x2y2)(x2y2)xy11xy22 x20.xx12.
xx12 y1y2 y1xx1y22 x1y2x2y10.
2.3.2
2 a(x1y1)b(x2y2)b0 x1y2 x2y10 ab.
b0x2y2 0 x20 x1y2
x2y10 y1xx12y2.
(x1y1)x1xx12y2xx12(x2y2)
xx12 ab. ab.
2.3.2
1 P1P2 (x1y1)(x2y2)
P1P2 P
P P1P2
P1PPP2
OPOP1OP2OP
OP12(OP1OP2)x12 x2y12 y2.
P1P2 x12 x2y12 y2.
2.3.2
2 P1P2 (x1y1)(x2y2) P P1P2 P
P P1P2
P1P13P1P2OPOP1P1POP113P1P2
OP113(OP2OP1)23OP113OP22x13x22y13y2
P1P23P1P2OPOP1P1POP123P1P2
OP123(OP2OP1)13OP123OP2x132x2y132y2.
3 ABC
A(x1y1)B(x2y2)C(x3y3)ABC G
AG BC D
G ABC
D BC
AG23AD2312AB12AC13AB13AC
OGOAAGOA13AB13AC
OA13(OBOA)13(OCOA)13(OAOBOC)
x1x32x3y1y32y3.
2.3.2
P P1P2 PP1PP2.
2.3.2
2.3.2
1
<1
1 1<<0 0
P
P1P2
P2P1 P1
P
2.3.2
0<<1
1
>1
P
P1
P
P2
P
2.3.2
2 P1(x1y1)P2(x2y2) P1P2
P(xy)
OPOP1P1POP1PP2
OP1(OP2OP)OP1OP2OP
OPOP11OP211 (x1y1)1 (x2y2)
11 x111 y11 x21 y2
x11x2y11y2.
Px11x2y11y2.
2.3.2
[]
1 a(1,2)b(3,2) k kab a
3b kabk(1,2)(3,2)(k3,2k2)
a3b(1,2)3(3,2)(104)
kab a3b
(k3)(4)10(2k2)0 k13.
kab13323213(a3b)
k13kab a3b
2.3.2
1 A(2,1)B(0,4)C(1,3)D(53)
ABCD
AB(0,4)(2,1)(2,3)
CD(53)(1,3)(46)
(2)(6)340
(2)4<0
ABCD
CD2ABABCD
2.3.2
2 A(11)B(1,3)C(2,5) ABC
ABOBOA(1,3)(11)(2,4)
ACOCOA(2,5)(11)(3,6)
26340ABAC.
ABAC A
ABC
2.3.2
2 A(1,2)B(2,4)C(3m)
m
AB (2,4)(1,2)(1,2)
AC(3m)(1,2)(2m2)
ABC ABAC
ABAC
(1,2)(2m2)(2m2)
2m122.
12 m6.
m6 ABC
2.3.2
3 A(34) B(1,2) P AB |AP| 2|PB| P
P (xy)
|AP|2|PB|AP2PBAP2PB.
AP2PB(x3y4)2(1x,2y)
xy 34 42 2y2x AP2PB
x13 y0
P 130.
(x3y4)2(1x,2y)
xy 34 242x2y xy 8 5 .
2.3.2
P (5,8)
P 130(5,8)
2.3.2
3 A(12)AB a(2,3)
|AB|2 13 B AB(xy)AB a
ABa (>0)(xy)(2,3)
xy23 |AB|2 13
x2y252.4292522 (>0)
AB(4,6) B (5,4)
2.3.2
1 a(1,2)b(2y) ab y _____4___
ab(1)y220y4.
2________
a1(2,3)b1(4,6) a2(12)b2(7,14)
a3(2,3)b3(3,2)
a4(3,2)b4(64)
6324a4b4.
2.3.2
2.3.2
3 A(11)B(1,3)C(x,5)ABBC
____2____
AB(2,4)BC(x1,2)
ABC ABBC 224(x1)0x2BC(1,2)
AB2BC2.
2.3.2
4OA(k,12)OB(4,5)OC(10k) A
BC k__2____1_1_. OA(k,12)OB(4,5)OC(10k)
AB(4k7)BC(6k5)
ABC
(4k)(k5)(7)60 k2 k11.
2.3.2
1
a(x1y1)b(x2y2)
(1) b0ab.
(2)x1y2x2y10.
(3) x2y20 xx12yy12
2.3.2
2
(1)
(2)