&$6$ !$ 91 & & & 5/ u X-IUI2I v X-%U%2% w X-KUK2K ) & & & / 0 u ⋅ (v × w) & F 0 (u & & , v , w) 73 / / )B1! y & & v×w = 2 y3 $! x z2 & ⋅i − 2 x3 z3 x z2 & ⋅j + 2 x3 z3 y2 & ⋅k y3 ) / y & & & u ⋅ (v × w) = x1 . 2 y3 )! x z2 + z1 . 2 x3 z3 x z2 − y1. 2 x3 z3 y2 y3 ) x1 & & & & & & u ⋅ (v × w) = (u , v , w) = x2 x3 $! y1 z1 y2 y3 z2 z3 & & & , v , w) = 0 ! % (u •/ [ & & & •$ u v w [ •$ & F (u & & , v , w) )/ & & & & & & $./ (u , v , w) XI&) (v , u , w) XOI& & & & ) (u , v , w) ! •C )/ ./ 7 •5 / )./ 7 )/ & & & & & & ? ! u ⋅ (v × w) = (u × v ) ⋅ w %&&V[$$X& $&$6$ !$ & & & * (u , v , w) 0 P 3 & & & / )3 u v w F1!B +X & & & (u , v , w) 2 (- +/ ! & & & u X%&& v X&E& w X&&M M 907/ / + / ) ) - 5+3/B ! BX7 F;( F* 5 K' ( E % 4 F BX%EM BXE&/cF!/→/d * - ; U & & & 8/ u v w ! 2 0 0 & & & B +X | (u , v , w) | = 0 7 0 = 2 . 7 .5 = 70 0 0 5 BXE&/ 5 - 0 ) 0 3 / ) B1! & & & $1 A B C D ) ) / u = AB v = AC w = AD 0 ) ) / ) +/1 -1/0! B +X ( AB , AC , AD) !B +X & & & (u , v , w) + /2 ;( /1 . / . 7 / +1! B = I % ⋅ B + /0 * / = /9 ;( = 7 ;(5 (/ =0 0IbK/ ! I B = ⋅ B K B = B = I K I N ⋅ I ⋅ B % + ⋅ B + B# X & 1 ⋅ (u& , v& , w ) 6 Q,$! 7($1I%OI;M&I(%OII5NIOK/0 3! (/[ 0( )0 [ ( //0 5 KJ ;(B I%L;OI&O%(&%%5O%IOK) &91 F A B C D ) ) / AB AC AD 0 /1-)/ ( AB, AC , AD) = 0 ?/ / / ! AB X B − A = (−1, 0, − 2) − (1, 2, 4) = (−2, − 2, − 6) D AC X C − A = (0, 2, 2) − (1, 2, 4) = (−1, 0, − 2) C A AD X D − A = (−2, 1, − 3) − (1, 2, 4) = (−3, − 1, − 7) ( / ! π −2 −2 −6 ( AB, AC , AD) = − 1 −3 0 − 2 = 0 − 12 − 6 − (0 − 4 − 14) = − 18 + 18 = 0 −1 − 7 ( ( AB, AC , AD) = 0 / )) @ A B C D ) Q&5 $!# & & 7(5/ u = (3, − 1, 1) v & & & v , w) ( (u , & & & ;($ u ⋅ (v × w) = & & & ( u ⋅ ( w × v ) & = (1, 2, 2) w = (2, 0, − 3) ! & & & 0( ( w, u , v ) 2 ! & & & 0( (u × w) ⋅ (3v ) & & & & & & & & & >(F/ + % 1 + KA % − 1 + A K + 1 + LA ) WD L& B