მასწავლებლის წიგნი

mniSvnelovania kavSiri veqtorebze moqmedebebsa da veqtoris koordinatebs Soris:Tu p=(x 1; y 1; z 1), q=(x 2; y 2; z 2), maSinp+q=(x 1+x 2; y 1+y 2; z 1+z 2);p – q=(x 1-x 2; y 1-y 2; z 1-z 2).Tu p=(x; y; z), α∈R,maSin αp=(αx; αy; αz).es faqtebi paragrafis Teoriul nawilSi debulebebis saxiTaa warmodgenili damaTi damtkicebisTvis gamoiyeneT veqtoris (*) warmodgena. SesaZlebelia damtkicebadafaze CavataroT da amisTvis romelime moswavle gamoviZaxoT, romelsac daevalebaklasSi mimdinare ganxilvis oponireba da dafaze asaxva.paragrafis meore nawilSi vixsenebT veqtorebis skalarul namravls:a ⋅ b =|a|⋅| b|⋅ cosϕ, sadac ϕ aris kuTxe a-sa da b-s Soris.skalaruli namravlis Tvisebebia:1) a ⋅ b = b ⋅ a2) (aa)⋅ b)=a(a⋅b), α∈R3) (a+b)⋅c=a ⋅ c+b ⋅ c4) (aa +bb)⋅ (gc +δd) =aga⋅c + ada⋅d + bgb⋅c + bdb⋅d, α, β, γ, δ∈R.mniSvnelovani Sedegia:Tu a=(x 1; y 1; z 1), b=(x 2; y 2; z 2), maSin a⋅b=x 1x 2+y 1y 2+z 1z 2.am faqtis damtkicebisas gamoviyenoT veqtoris (*) warmodgena da skalaruli namravlisTvisebebi:a =x 1i +y 1j +z 1k, b =x 2i +y 2j +z 2ka ⋅ b =x 1x 2i ⋅ i +x 1y 2i ⋅ j +x 1z 2i ⋅k+y 1x 2j ⋅ i +y 1y 2j ⋅ j +y 1z 2j ⋅k+z 1x 2k⋅ i +z 1y 2k⋅ j +z 1z 2k⋅k.Tu gaviTvaliswinebT, rom i , j , k wyvil-wyvilad marTobuli ortebiai ⋅ j = i ⋅k=...=k⋅ j =0:amasTanave, i ⋅ i = j ⋅ j =k⋅k=1, maSin miviRebT;a ⋅ b =x 1x 2+y 1y 2+z 1z 2.am formulis gamoyenebiT miiReba or veqtors Soris kuTxis kosinusis gamosaxulebaveqtorebis koordinatebis saSualebiT:xcosϕ=1x 2+y 1y 2+z 1z 2.2√x12 +y 12+z 12√x 22+y 22+z 2SevniSnoT, rom a da b aranulovani veqtorebi TanamimarTulia mxolod maSin,roca cosϕ=1; sawinaaRmdegodaa mimarTuli _ roca cosϕ=–1 da marTobulia, rocacosϕ=0, anu x 1x 2+y 1y 2+z 1z 2=0.37