Wedzera vhekita nenhamba

Muchinyorwa chino, tichaona kuti vhekita inogona kuwanzwa sei nenhamba (kududzira geometric uye algebraic formula). Isu tinonyorawo zvimiro zvechiito ichi uye tinoongorora mienzaniso yemabasa.

gutsikana

Geometric dudziro yebasa

Kana iyo vector a wedzerai nenhamba m, wobva wawana vector b, umo:

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

Saka, chigadzirwa cheiyo isiri-zero vector nenhamba ndeye vector:

  • colinear kune yekutanga;
  • co-directional (kana nhamba yakakura kupfuura zero) kana kuva nedivi rinopesana (kana nhamba iri pasi pe zero);
  • Hurefu hwakaenzana nehurefu hwevheji yekupinza yakapetwa ne modulus yenhamba.

Formula yekuwanza vhekita nenhamba

Chigadzirwa chenon-zero vector nenhamba ivhekita ine makonarisheni akaenzana neanoenderana macoordinates eiyo yekutanga vector, yakapetwa nenhamba yakapihwa.

Zvemabasa akapfavaKwe XNUMXD mabasaKune n-dimensional vectorsСвойства 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)
  • 1 · a = a
  • 0 · a = 0

Mienzaniso yebasa

Basa 1

Найдем произведение вектора a = {5; 11} uye chinyorwa 4.

mhinduro:

4 · a = {4 · 5; 4 · 11} = {20; 44}

Basa 2

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

mhinduro:

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

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