Let      (as/Kt/ig be  a real vecčor &ptce~
ifowjßw/o of U   mil fee   called   sometimes., pot*H
Affľhtz cubs pace, of If     (s a no*e*n 6-^ subset of   14   of  the, forw Vis called the direction
, č>f m and tie m ted 20r>)\
W-fotz,   h e Ol £$ *L point V ^14 i& « vecéor
/s    so called fHr*»ietm description   of £ 2-rf/i#i. 4 (fine su b £ face,  ( jol<?t>e)  ^/Ve*  fc^ 6Jje M - C c?,  2<*J   <%v\ol the vector culozpaie-
Eia\n?\e. t   14* ^    ne ^ of all sola hens of  b\e C^teto  of  linear efnaú*e»$
4**f -2 y*       -      Ä r
^p,e I/ * fr*e  fee ^ ***
the homoq^neěds
Leh U be. a real vector space  m'ih  4, sea lair pra otwk      ^ ,  >  ; H + 14 —y JR
The distance  of   tvco pofu fcs   A tJš       i's the tiovy» of  the   vector    3-A
últst ( Á i B ) - // 3-A í - Í<A-b/Ä-
sjoace  ^   ii  denned a$>
We confute* this. diQbahce. usľnq an erthoqenat pro /e cti ens.
Theorem 1
(öS)  TM, &tista*crs. of a point A   f rem an affine subside  ^ * St?:i%)  is efm/ to the nerv* o f the crbho^oml   f refection   of the. veCtov A-£   to  the $>f*<x> .
(lo)   "The  f-olfavfi'na   4 sse-rfci'irMi;   «re <&f-Klent (<)       ^fc  í A,       - li A-fill  f-eir * feint h z
* A
--<^
Vit, *p«airty   occurs  jus 6 f er    v - ?^'B) ■ Hebte,
odít       = M>'n 11A-n »«^».ij. ÍA'B^l
yen, *" u
ftroef- o f £>) OMitbzčH £j
^e ^is^nec  of affine......g,ŕgc_<gs   ^ <W ^
okULm.V) = M/m  [rfi-st ÍX.V)^ Xe^f,r&^íJ \Tb holds : /f ^ = fl/ 2/*?), ^»£t2/4)
Mist í H, %) ^ mľnfa'st (A-fA-> Bt""") / we- 2A)j
liehce    we qeb
THEOREM        (a) The distance   yetuy^eh W^AtZ/fyJ ahd. 4t * B * ~2rl?u)  is the* norm   of the crthoqo-nat  Tf>ro^e,cbiov\   #f the vector  A-B into (2(ft) t 27*^"^
(b)   The folleivi'yiq   desertions,  f&ir fc/'nts h&/Wl Cz)     h- N    J_    2-/^?)t tin)
F<pr M= 7R* cotofmte. the c4isbzhc<^ o-f <x ]f>o\nh   A = Cx,, yt/ yi; yv) t J^^/ofeJie
Solution  :     Ot'st ( At%) ^   II IA ~B) II
for a feint    £ £ *?£ .   /*r£ *s   cheoz^ B*^}0,0-jS\
2:1%)    : * *ctfv**<^ «£?
We.  £«? m p6t fc e    fc-he otb^xo^oVi^C   fire jetton r    *f bh*  vector   AS   *C *tt*h *i{
into z-inr)*-
- s~-
Atopie V f1* <Tí>w    6-e  íAe ^íir6A«ce
W the ři«ep :
* = (e;tíSll)/   A/* (3, Z, 1,0))
tíomev/of\c 6   Cotopnye.   the di'sbtkee* t?-f- k*v (otenes
Ahqlez   between    <gf£ihe   &14 fc>spaces
f) The tfn<y/e   kx^tween   é^c? //«es
w^Pie^e tf*čf v^č*  /s    -5. (ď]) ^ ocer^rj
SkčA   that , y
cos* ~ e CM]
/I U U Uvit
© Tlie an^le   ]pehweeh   t\»o  Vecber Suks\o4ces. V and. W such   bb&b       V n W - -Lô^ /s
Q   The^le-   be^eeh   -fr^   vector ^tbef*'**
^ ^ W)   =- ^ (V^^, UM""^) nn a»oí -Ti /'s
Theorem S Leh n*if*i?J. a^ Vt's 4 c«hef*<e. of   (j Then
rnv\ IIT^" co& ^ CM, v) =
Whete: 'Vy is tke otbko^cwí projection oh the vector zub&pace, V
'Vroo^   Ipq   <z picture-
MS
Theo\rev« if      The anqle  bet^ee*  a line a*\d
a hc^ pev^p [dine   (   h<jpev^khe {& ah ^ff/'we
£ u b c pace,  o£ c*\m  k-1   í'h the £f><*ce <s>f /ij
/S X   - the av\<$le   betwee  the i í Vie
tt
£%<Zfaj>le,     lA-     *   vcikh ctáhonoriveit leasts
a** the plane,   p.- *ŕí^-V«>W4*,-V'*)
Monte vor L 7_    compute   the* o-hql-e bebiie/^ee^
i