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# 【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

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)