Chulukitsani vekitala ndi nambala

M'bukuli, tiwona momwe vector ingachulukitsire ndi nambala (kutanthauzira kwa geometric ndi algebraic formula). Timalembanso zinthu zomwe zimachitika izi ndikusanthula zitsanzo za ntchito.

Timasangalala

Kutanthauzira kwa geometric ntchito

Ngati vekitala a chulukitsani ndi nambala m, ndiye mupeza vekitala b, pamene:

  • b || a
  • |b| | = |m| · |a|
  • b ↑↑ angati m> 0, b ↑ ↓ angati m <0

Chifukwa chake, chopangidwa ndi vekitala yopanda ziro ndi nambala ndi vekitala:

  • colinear kwa choyambirira;
  • co-directional (ngati chiwerengerocho ndi chachikulu kuposa ziro) kapena kukhala ndi mbali ina (ngati chiwerengerocho ndi chocheperapo);
  • Utali wake ndi wofanana ndi kutalika kwa cholowetsa cholowetsamo chochulukitsa ndi modulus ya nambala.

Njira yochulukitsa vekitala ndi nambala

Chopangidwa ndi vekitala yopanda ziro ndi nambala ndi vekitala yomwe makonzedwe ake ali ofanana ndi ma coordinates a vekitala yoyambirira, yochulukitsidwa ndi nambala yoperekedwa.

Kwa ntchito zopanda pakeKwa ntchito za XNUMXDKwa ma vector a n-dimensionalСвойства произведения вектора ndi числа

Для любых произвольных векторов ndi чисел:

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

Mavuto a zitsanzo

Ntchito 1

Найдем произведение вектора a = {5; 11} ndi gawo 4.

yankho;

4 · a = {4 · 5; 4 · 11} = {20; 44}

Ntchito 2

Умножим вектор b = {2; -4; 7} pa chисло -6.

yankho;

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

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