Page 236 - Math Grade 11 (Advance)
P. 236

PROEUS DARA


                  8  m'!§dt~t1htt:nru1u9~ t  2h  t  '1
                        1 A   i-J   1
                          1
                - nhtfflru~H'inruTJnH~Hl.ltfl  r:lru~n.nn.nt'rutsri~1u9~ it=  (x,  y,  z)  2h
                  .,         u u                 1   n         1
                   1
                   7             ~  ~  7
                   v  = (x',  y',  z')  ~ u · v  = xx' + yy' + zz'  '1
                n.  ri~lu&lj it=  (x.  y,  z)  2h  t = (x',  y',  z')  ~~~~ruTJru~ npunt'~ it· t = o
                    ens S rum  ft_L t  tu'i:1'i:Hli  xx' + yy' + zz'  =  0  '1
                                       u
                          eJ   Q!q_    ':1   ~   C)   7      0   I
                2.  filtHt.mru  Sw  nil'\5  ~s~u9~ u  =  (x,  y,  z)  nrul~tt:nru
                        n                1
                    ~2   2   2   2  .,. 14  I ~  J 2   2   2
                   U  =X  + y  + Z   2w  U  1  =  X  + y  + Z  '1
                                                                ~
                                                                                  '
                ~.  r:lru~n.nn.nt'rutsth1u9j-@stus'i t, t  2h'!§  8  ( ~ntillll:jJh ) nrulntt:n ru
                                                                             0
                                                                     01
                                                                          •
                       1   n         1       u  u         1
                                                  it· t
                          1~1  171
                   u · v  =  u  ·  v cosEl  sn2J  cosEl  = litl·ltl  = J   xx' + yy' + zz'   '1
                                                                      J
                                      o
                    ~  7
                                                                             2
                                                                        2
                                                            2
                                                                2
                                                           x  + y  + z  2   x'  + y'  + z'  2
                - uH'lrultlh  P  sh  Q  nrultitt:nru
                                       0
                                "'
                                           '
                    "'
                                           2         2         2
                  d(P,  Q)  = PQ  =  j(x -x ) +(y -y ) +(z -z )  '1
                                                   1
                                                             1
                                                2
                                                         2
                                          1
                                      2
                - tu~ffUt2thlatl:jillH120n'i~~ (a,  b,  c)  2hm  r  ~
                             &         .:.  l.i
                        2       2        2   2
                  (x-a) +(y-b) +(z-c) =  r     '1
                  1u9~9mh ~  tSGrulu  C  tl:jrutun~~~ [AB]  :nhQhffl'!:1r:lrumJu  m:  n  ?f
                   1    ~   ~        1                             1
                  ~ =  mb+na  '1
                        m+n
                - 1u9~9mh ~  t2Grulu  D  tl:jrutun~~~ [AB]  :nhq_,niffl'!:1r:lrumJu  m:  n  ?f
                   1    ~   ~       I
                  d =  mb-na  '1
                        m-n
                  ti5~fflm~~ (L)  ffl~ffl'i:1G'l.f1u  P (x ,  y ,  z )  Ln1m9ishlu9~Lcnti9ti5
                                                    0
                                                        0
                                                           0
                                                  0
                   ~            ~ x - x 0   y -Yo   z - z 0
                  u  =  (a,  b,  c)  ~ -- =  -b- =  -- '1
                                    a              c
                - tu~fflm~~ffl~ffl'!:1[ht3'l.f1u  P (x ,  y ,  z )  2h  P (x ,  y ,  z )  ?f
                                               0
                                                                      1
                                                                1
                                                                   1
                                                                          1
                                                        0
                                                     0
                                                 0
                   x-x     y-y 0    z-z 0
                       0
                  --=--=-- '1
                  xi-xo    YI-Yo    zi-zo
                    Ca,l   I  eJ   0   I   0                   Q   ~   C)   "   '  7
                - ti5'!:1ffl~~btfjruf1rul~Ht:hruu'l.f1u  P (x ,  y ,  z )  2h•ulfirulaH'lru  n  =  (a,  b,  c)
                                                  0
                                                            0
                                                        0
                                                     0
                                                                  1
                   H12llh  ax+by+cz+d = 0
                - MrulGrulu  Q(x,  y,  z)  tdlbm~ti5~ffl~ ax+by+cz+d = 0  (  tl:jru  a,  b,  c,  d
                      I   1              ~.,;
                   mcrsstin  n.f\ru  a,  b,  c  @sti52'1Ut1'!:1ffl)  ~tilti~tl:jruH1s1u9~n.nfihru
                      IJ                       u  u   "'      G\1        1
                   ~
                  n  = (a,  b,  c)  '1
                                                                                         231
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