.

1

1.

1.1 2 1. (Scalar quantity)

2. (Vector quantity)

B

A

ABJJJG A B u , v , w | |AB | |u

1.2 1) 2) u u u

u 3) 0 0 4)

AC AB BC= +JJJG JJJG JJJG ( )AB AC BC AC BC= = + JJJG JJJG JJJG JJJG JJJG

5) u v v u+ = + , ( ) (u v w v u w)+ + = + +

6) u c - c > 0 cu c|u | u

2

- c < 0 cu c|u | u

7) , u v c u cv=

1 3 2 2 4 4 4AB BC CD ED EF AF BA DA+ + + + JJJG JJJG JJJG JJJG JJJG JJJG JJJG JJJG 2 0u 0v u v ) 2v u v= + ) 3

2v v u=

) 3v cu v u+ = 1c > ) 3 2 4 2u v v = u

3

2.

2.1 (0,0) A(a,b) aOA

b =

JJJG

2.2 (0,0,0)

A(a,b,c) a

OA bc

=

JJJG

A(a,b)

A(a,b,c)

4

2.3 11

au

b =

22

av

b =

1) 11

au

b =

2) 1 21 2

a au v

b b+ + = +

3) 11

cacu

cb =

4) 2 21 1| |u a b= + 5) u 1

2 211 1

1 aba b +

2.4

100

i =

010

j =

001

k =

a

u bc

= u ai b j ck= + +

3 A, B, C O 3 2OA i j= JJJG 2 5OB i j= +JJJG 2

3AC A= BJJJG JJJG 2|OC |JJJG

5

3.

3.1 a

u bc

= x y

z , ,| | | | | |a b cu u u

u x y z 3.2

4 0

31

u =

) u 60 x ) u 30 y ) u 30 z ) u 60 y

6

4.

4.1 u v u v u v | || | cosu v u v =

1

1

1

au b

c

=

2

2

2

av b

c

= 1 2 1 2 1 2u v a a bb c c = + +

4.2 1) u v v u = 2) ( )u v w u v u w + = + 3) 2| |u u= u 4) u v 0u v = 5) u v | || |u v u v =6) 2 2 2| | | | | | 2u v u v u v+ = + + 7) 2 2 2| | | | | | 2u v u v u v = +

5 25

u 12

v = 11u w = 8v w = = | |

w v

7

6 3 4 2u i j k= + 2v i j k= + sin

4.3 1) ( )u v v u = 2) ( ) ( ) ( )w u v u w + = + u v 3) ( ) ( )cu v c u v = 4) ( ) ( )u v w u v w = 5) | | | || | sinu v u v = u v 6) u v u v u v

5.

ABCD ABCD = | |AB ADJJJG JJJG = | || | sinAB AD JJJG JJJG

6.

u , v w | ( )w u v |

8

7 3 2u i j= + , 2v i k= w j k=

1. ABC D AC F BC 1

4AD A=JJJG JJJGC , 1

3BF BC=JJJG JJJG DF aAB bBC= +JJJG JJJG JJJG a

b

9

2. u v u v

u v+ u v ) | | | |u v= ) 2u + v 2u v

3. u v 3u i j= + , | | 3v = | |u v = 4 | |u v+) 6 ) 10 ) 13 ) 4

10

4. 2 5u i j= , 2v i j= + , 11u w = 8v w = w 5i j+ tan sin 2 +

5. u xi y j= + , 4 3v i j= 2w i j= + 2 2 2| | | |u v u v = +

1| |

5 5 2x y+ = u w ) 5 ) 6 3) 10 4) 14

11

6. ) 2( ) ( )(u v u u v v ) ) 2( ) (| || |)u v u v = 2 u v ) 0u v w , + + = | | 3u = , | | 4v = | | 7w = 12u v = ) 2 2 2| | | |u v u v = | |