Amaway (tusnakt d tfizikt )

Amaway d tɣawsa tagejdant deg tusnakt, ladɣa deg tanzeggit tusliḍt d tusna n yigazen. Yettwaɛqal s teɣzi-ines d tanila-ines.

Tadabut

Amaway d tɣawsa tusnakt yesɛan teɣzi d tanila. Yezmer ad yettwammel s useqdec n yimsidag deg unagraw n yimsidag, neɣ s useqdec n teɣzi d yikusinusen inilayen.

Imawayen tigget

Llan kraḍ n yimawayen tigget deg unagraw n yimsidag s kraḍ n tsektiwin:

Yal amaway tigget yesɛa teɣzi n 1:

|𝑖 | = |𝑗 | = |𝑘⃗ | = 1

Imsidag n umaway

Amaway 𝑢⃗ yezmer ad yettwammel s yimsidag-ines:

u → = ( X , Y , Z ) {\displaystyle {\vec {u}}=(X,Y,Z)}

Anda X, Y, d Z d imsidag n umaway 𝑢⃗ deg unagraw n yimsidag s kraḍ n tsektiwin.

Teɣzi n umaway

Teɣzi n umaway 𝑢⃗ tettwasuḍen s:

| u → | = X 2 + Y 2 + Z 2 {\displaystyle |{\vec {u}}|={\sqrt {X^{2}+Y^{2}+Z^{2}}}}

Tiɣmert gar sin n yimawayen

Tiɣmert θ gar sin n yimawayen 𝑢⃗ d 𝑣 tezmer ad tettwammel s:

cos θ = (𝑢⃗ · 𝑣 ) / (|𝑢⃗ | |𝑣 |)

Anda 𝑢⃗ · 𝑣 d afaris n sin yimawayen.

Timernit n yimawayen

Timernit n sin yimawayen 𝑢⃗ d 𝑣 tettili s tmernit n yimsidag-nsen:

𝑢⃗ + 𝑣 = (X1 + X2, Y1 + Y2, Z1 + Z2)

Timernit n yimawayen tesɛa sin yisuḍaf igejdanen:

Tukksa n yimawayen

Tukksa n yimawayen tettili s tukksa n yimsidag-nsen:

𝑢⃗ - 𝑣 = (X1 - X2, Y1 - Y2, Z1 - Z2)

Amaway gar sin yigazen

Amaway gar sin yigazen A(x0, y0, z0) d B(x1, y1, z1) yettwaḥsab s:

𝑟 = 𝐴𝐵⃗⃗⃗⃗⃗ = (x1 - x0)𝑖 + (y1 - y0)𝑗 + (z1 - z0)𝑘⃗

Teɣzi n umaway-a tettwaḥsab s:

|𝑟 | = |𝐴𝐵⃗⃗⃗⃗⃗ | = √((x1 - x0)² + (y1 - y0)² + (z1 - z0)²)

Ikusinusen inilayen

Ikusinusen inilayen n umaway 𝑟 d:

Anda X, Y, d Z d imsidag n umaway 𝑟 .

Iseqdacen n yimawayen

Imawayen ttwafen deg waṭas n yisenfaren n tusna d tejjunant: