Whakareatia te vector ki te tau

I roto i tenei whakaputanga, ka whakaaro tatou me pehea te whakarea o te vector ki te tau (te whakamaori ahuahanga me te tauira taurangi). Ka whakarārangihia hoki e mātou ngā āhuatanga o tēnei mahi me te tātari i ngā tauira mahi.

ihirangi

Te whakamaoritanga ahuahanga o te mahi

Mena ko te vector a whakareatia ki te tau m, ka whiwhi koe i te vector b, kei roto:

  • b || a
  • |b| = |m| · |a|
  • b ↑↑ a, ki te m > 0, b ↑ ↓ aki te m <0

No reira, ko te hua o te vector kore-kore ma te tau he vector:

  • collinear ki te taketake;
  • te aronga tahi (mehemea he nui ake te tau i te kore) he huarahi rereke ranei (mehemea he iti iho te tau i te kore);
  • He rite te roa ki te roa o te vector tāuru kua whakareatia ki te kōwae o te tau.

Ko te tātai hei whakarea i te vector ki te tau

Te hua o te vector kore-kore ma te tau he vector e rite ana ona taunga ki nga taunga o te vector taketake, ka whakareatia ki tetahi tau.

Mo nga mahi papatahiMo nga mahi XNUMXDMo nga vector ahu-nСвойства произведения вектора и числа

Для любых произвольных векторов и чисел:

  • (m ± n) · a = m · a ± n · a
  • m · (a ± b) = m · a ± m · b
  • m · (n · a) = (m · n) · a = n · (m · a)
  • a = a
  • a = 0

Tauira raruraru

Mahi Mahi 1

Найдем произведение вектора a = {5; 11} me te tohu 4.

otinga:

a = {4 · 5; 4 · 11} = {20; 44}

Mahi Mahi 2

Умножим вектор b = {2; -4; 7} на число -6.

otinga:

-6 · b = {(-6) · 2; (-6) · (-4); (-6) · 7} = {-12; 24; -42}.

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  • Ngā vector orthogonal

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