Kuphatikizika kwa ma vector

M'buku lino, tiwona momwe tingapezere mtanda wa ma vector awiri, kupereka kutanthauzira kwa geometric, algebraic formula ndi katundu wa izi, komanso kusanthula chitsanzo cha kuthetsa vutoli.

Kutanthauzira kwa geometric

Chopangidwa ndi ma vector awiri osakhala ziro a и b ndi vekitala c, zomwe zimatchulidwa kuti [a, b] or a x b.

Kutalika kwa Vector c ndi lofanana ndi dera la parallelogram yomangidwa pogwiritsa ntchito ma vector a и b.

Pamenepa, c perpendicular kwa ndege yomwe iwo ali a и b, ndipo ili kuti kasinthasintha pang'ono kuchokera a к b zidachitika motsatana (kuchokera kumapeto kwa vekitala).

Cross mankhwala chilinganizo

Zopangidwa ndi ma vector a = {a_x; kuti_y,_z} ndi b = {b_x; b_y,b_z} iwerengedwa pogwiritsa ntchito imodzi mwa njira zotsatirazi:

Cross mankhwala katundu

1. Kuphatikizika kwa ma vector awiri omwe sanali ziro ndi ofanana ndi ziro ngati ndipo kokha ngati ma vector awa ali collinear.

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

2. Gawo la mtanda wa ma vector awiri ndi ofanana ndi gawo la parallelogram yopangidwa ndi ma vector awa.

S_kufanana = |a x b|

3. Malo a makona atatu opangidwa ndi ma vector awiri ndi ofanana ndi theka la mankhwala awo a vector.

S_Δ = ¹/₂ · |a x b|

4. Vector yomwe ili yopangidwa ndi ma vector ena awiri ndi perpendicular kwa iwo.

c ⟂ a, c ⟂ b.

5. a x b =-b x a

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

7.a + bx) c = a x c + b x c

Chitsanzo cha vuto

Kuwerengera mtanda mankhwala a = {2; 4; 5} и b = {9; - ziwiri; 3}.

Kusankha:

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