IE Ft29y=mxtn n # q=pyq Lines -1=5 +2 : egg line LY - PDF document

oEegeometyaadlinearaCge8# 1/3 in the place points in the plane Vectors : : - : :÷÷÷÷÷÷÷ . i¥÷÷i÷i÷÷÷:÷÷÷ 44 a " a ' Et a generalization of a point - , Y y - up ) we have :S - l 's ) - Eta I - a- - ftp.HH-EI.is ) E- l 'd { =L } ) = I - I Or in other words : a- = IE µ Ft29y=mxtn n # • q=pyq Lines -1=5 × +2 : egg line LY eR4y=Ixtz} z - p y i-TH But Houtorepreseat vertical lines ? §=( E) E- E) HEH 'D E- if Another way to describe this line : ( SERJ - steps -51 SERJ =L Fts - ( off ) 1=44 IE - affine combination direction vector = =L Sipe Sig ( syszEIRausitsz-BLiheseguey-tp-g-LU-slpts.ci/st5o,D } - 5-0 : Fto - g- =D " liheerihtrpoktionfetveeg ⇐ 0.4 : . . . -_ of Baudot o.p-ts.gr 4 5- I : Three points ;pTgYT : Trieste S , -152-(53--1) / sysz , Szeto ,D - g- TST - Lsiptsz and pain ÷ :* , III : mass . . - CHkpyypidqffgsipilsittoidau.ES . npointsp ,h' it } . Need to prove equihua to our other definition Alternative characterization .

2/3 Orientation test Ihalfplaukst ; - e.EE#::e.EiLeftthm( Right turn ( negating zero positive ) on leffsideofl rliesoh right side off relies usethesignoftheonertedareaofspqr.LT , # E- it " TE Yam :p :3 :£m ? ssajoqsyeaseiscouud.am :{ ¥ :{ ÷÷I :& .me b- signatory 's i' . det ( I } - K ⑧ - ay = ax.by signed area of parallelogram - - area of spgrt-tzdetfagYJJ-tzdetfgy.ie ⇒ signed - ok , I 9 qx - Ugx - I \ - (4-9 × 1) - lay - py ) - e) fry ' ' agg ) - ⑧ ztfgkry-qgrx-fpxry-pyrxp-pxgg-qxpyJ-aa.li#..::.l--tl' - - Might ÷i÷ti÷÷÷ ' :* . ÷a÷:¥÷¥iH÷ - I Area of ofxtsxkagtbg ) by b - y # - I though sx ⑤ ag - xay ay - - = axby - bxay

⇒ . ( 9g ! ) = ( Ppt ) 3/3 : f. of Scakrprodhct , t prop pig = l l F H = pv.fm Length of ¥÷:> vector : a 9 interpretation f. of = HOTH . It pull Geometric Cos a . - a ,¥w% - projection , of p onto 9 side opposite cos ← adjacent * potehhse F - 5=115/1 . Npg . cosy a ⇒ a=cosj¥ also in Rd Works - Another characterization of a line l ; peril t.EE?s--tF4R4 "÷÷÷÷f¥yI - e . e- constant - vectors whose projection onto g- has fixed length set of all it , e characterize hyperplane ⇒ Same definition works in Rd to using their normal vector - 9 . -