12
 เอกสารประกอบการสอน เว เตอร ดร.พล นวลทอง ภาคว ชาคณ ตศาสตร และสถ  คณะว ทยาศาสตร  มหาว ทยาล ยสงขลานคร นทร  ทยาเขตหาดใหญ  

vector.pdf

  • Upload
    top2

  • View
    12

  • Download
    0

Embed Size (px)

Citation preview

  • .

  • 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 = | |