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# 空间向量及其线性运算课件

B A D C

2、平面向量的加法、减法与数乘运算

b a

b a

a b a

ka ka

(k>0) (k<0)

3、平面向量的加法、减法与数乘运算律

a+b =b+a ( a + b) + c = a + (b + c ) k ( a + b) = k a＋k b

( a + b ) + c = a + (b + c ) 数乘分配律 k ( a + b ) = k a＋ k b

( a + b ) + c = a + (b + c ) 数乘分配律

k ( a + b ) = k a＋ k b

CB + BA1 = CA1

A C

1 AC + CB + AA1 = AM 2

B

AA1 ? AC ? CB = BA1

3 OE = i + 4 j 2
3 OF = i + 4 j + 2k 2

(1) AB + BC ( 2 ) AB + AD + AA 1 1 ( 3) ( AB + AD + AA 1 ) 3 1 ( 4 ) AB + AD + CC 1 2

A D B A1 G C D1 B1 M C1

( 2 ) AB + AD + AA 1 = AC + AA 1 = AC + CC 1 = AC 1

(1) AB1 + A1 D1 + C1C = x AC

= AB1 + B1C1 + C1C
A1

D1 B1

C1

= AC ∴ x = 1.
A

D B

C

( 2) 2 AD1 ? BD1 = x AC 1 (3) AC + AB1 + AD1 = x AC 1

( 2) 2 AD1 ? BD1 = x AC1
( 2 ) 2 AD 1 ? BD 1
= AD1 + ( BC1 ? BD1 ) = AD1 + D1C1 = AC1
A1 D1 B1 C1

∴ x = 1.
A

D B

C

(3) AC + AB1 + AD1 = x AC 1

(3) AC + AB1 + AD1
= ( AD + AB) + ( AA1 + AB) + ( AA1 + AD)
= 2( AD + AB + AA1 ) = 2AC1
D1 A1 B1 C1

∴ x = 2.
A

D B

C

1 (1) AB + ( BC + BD) 2 1 (2) AG ? ( AB + AC ) 2
D G

(1)原式＝AB + BM + MG = AG
(2)原式
1 ＝ AB + BM + MG ? ( AB + AC ) 2 1 ＝ BM + MG + ( AB ? AC ) 2 ＝BM + MG+ MB = MG

B

M

C

D

(1)AC = x(AB+ BC+ CC )
' ' '

(2)AE= AA + xAB+ yAD

A

D

B

C

D

(1)AC = x(AB+ BC+ CC )
' ' '

(2)AE= AA + xAB+ yAD

A

D

B

C

D

(2)AE= AA + xAB+ yAD
'

A

D

B

C

( a + b ) + c = a + (b + c ) 数乘分配律
k ( a + b ) = k a＋ k b

( a + b ) + c = a + (b + c )

k ( a + b ) = k a＋ k b

### (学案)空间向量及其线性运算

(学案)空间向量及其线性运算_高二数学_数学_高中教育_教育专区。空间向量学案3.1...(本节是课件) [教学过程]: 一、创设情景 1、平面向量的概念及其运算法则; 2...