Hua whiti o nga vectors

I roto i tenei whakaputanga, ka whai whakaaro tatou me pehea te kimi i te hua whiti o nga vector e rua, ka hoatu he whakamaarama ahuahanga, he tauira taurangi me nga ahuatanga o tenei hohenga, me te tātari hoki i tetahi tauira o te whakaoti rapanga.

Te whakamaoritanga ahuahanga

Hua Vector o nga vector kore-kore e rua a и b he vector c, e tohuhia ana hei [a, b] or a x b.

Te roa o te vector c he rite ki te horahanga o te whakarara i hangaia ma te whakamahi i nga vectors a и b.

I roto i tenei take, c e hāngai ana ki te rererangi kei reira a и b, a kei te noho kia iti rawa te hurihanga mai a к b i mahia ki te taha karaka (mai i te tirohanga o te pito o te vector).

Ripeka hua tātai

Hua o vectors a = {a_x; ki_y,_z} i b = {b_x; b_ypē b_z} ka tatauhia ma te whakamahi i tetahi o nga tauira i raro nei:

Nga hua whakawhiti

1. Ko te hua whiti o nga vector kore-kore e rua he rite ki te kore mena mena he collinear enei vectors.

[a, b] = 0, mena a || b.

2. Ko te kōwae o te hua ripeka o nga vectors e rua he rite ki te horahanga o te whakarara i hangaia e enei vectors.

S_whakarara = |a x b|

3. Ko te horahanga o te tapatoru i hangaia e nga vectors e rua e rite ana ki te haurua o te huanga vector.

S_Δ = ¹/₂ · |a x b|

4. He huanga whitinga o etahi atu vector e rua e noho tika ana ki a raua.

c ⟂ a, c ⟂ b.

5. a x b = –b x a

6. (m a) x a = a x (m b) = m (a x b)

kotahi. (a + b) x c = a x c + b x c

He tauira o te raruraru

Tatauhia te hua whiti a = {2; 4; 5} и b = {9; -rua; 3}.

Te whakatau:

whakahoki: a x b = {19; 43; -42}.