Vectors-ka cutubyada - dhibaatooyinka iyo xalalka

Vectors-ka cutubyada - dhibaatooyinka iyo xalalka

1. Shay wuxuu ku socdaa xawaare ah v = (2i − 1.5j) m/s. Waa maxay kala-guurka shayga 4 ilbiriqsi ka dib?

La yaqaan:

Qaybta toosan ee xawaaraha (v _x ) = 2 m/s

Qaybta toosan ee xawaaraha (v _y ) = 1.5 m/s

Muddada (t) = 4 ilbiriqsi

La Raadinayo: Barakac

Xalka:

Natiijada xawaaraha (v):

Barakaca:

s = vt = (2.5 m/s)(4 ilbiriqsi)

s = 10 mitir

2. Vektor F ₁ = 14 N iyo F ₂ = 10 N. Go'aami vektor-ka natiijada leh haddii lagu sheegay R = i + j.

Xalka:

Qaybaha vector-ka:

F _1x = (F ₁ )(cos 60 ^o ) = (14)(0.5) = -7 N (Taban sababtoo ah qaybtan vector-ka waxay tilmaamaysaa dhidibka x ee taban (bidix))

F _1y = (F ₁ )(sin 60 ^o ) = (14)(0.5√3) = 7√3 N (Togan sababtoo ah qaybtan vector-ka waxay tilmaamaysaa dhidibka y ee togan (midig))

F _2x = 10 N

F _2y = 0

Qaybaha ka mid ah fallaadhaha natiijada:

F _x = F _1x + F _2x + F _3x = -7 + 10 = 3 N

F _y = F _1y + F _2y + F _3y = 7√3 + 0 = 7√3 N

Vektor-ka natiijada ka soo baxda ee vektor-ka cutubka:

R = 3 i + 7√3 j

1. Waa maxay vektor-ka cutubka? Jawaab: Vektor cutub waa vektor leh cabbir dhan 1. Caadiyan wuxuu matalaa jihada isagoon gudbin wax macluumaad ah oo ku saabsan baaxadda.
2. Maxay vektorrada cutubyadu muhiim ugu yihiin xisaabta iyo fiisigiska vektorrada? Jawaab: Vektorrada cutubyadu waa lama huraan sababtoo ah waxay bixiyaan hab caadi ah oo lagu qeexo tilmaamaha. Waxaa lagu cabbiri karaa cabbir si loo soo saaro vekto dherer la rabo jiho gaar ah.
3. Sidee baad uga heli kartaa vektor cutub ah vektor la siiyay? Jawaab: Halbeeg halbeeg ah oo u jeeda halbeeg la bixiyay waxaa lagu heli karaa iyadoo loo qaybiyo halbeegga cabbirkiisa.
4. Waa maxay vector-yada cutubyada caadiga ah ee isku-duwayaasha Cartesian, maxayse yihiin tilmaamahooda? JawaabVectors-ka cutubka caadiga ah ee isku-duwayaasha Cartesian waa i, j, Iyo k. i tilmaama jihada dhidibka x, j tilmaamaya jihada dhidibka y, iyo k waxay tilmaamaysaa jihada dhidibka z.
5. Vektor-ka cutubku ma yeelan karaa qaybo aan ahayn 1 ama -1? Jawaab: Haa. Qaybaha vektor-ka cutubku waxay ku xiran yihiin jihadiisa. Vektor-yada cutubka oo keliya ayaa la jaanqaadaya dhidibyada isku-duwayaasha (sida i, j, k isku-duwayaasha Cartesian) waxay yeelan doonaan qaybo ka mid ah 1, -1, ama 0.
6. Wadarta laba vectors-ka cutub ma daruuri baa inay tahay vector-ka cutubka? Jawaab: Maya. Wadarta laba vectors-ka cutub guud ahaan ma aha vector halbeeg ilaa labada vector ay yihiin kuwo isku xiran oo si liddi ah u jiheysan.
7. Vektor cutub ma la miisaami karaa si uu u matalo vektor leh cabbir kala duwan laakiin jiho isku mid ah? Jawaab: Haa. Ku dhufashada vektor cutubka scalar waxay beddeli doontaa baaxaddeeda iyadoo jihada ay isku mid tahay.
8. Waa maxay baaxadda wax soo saarka isdhaafka ah ee laba vectors-ka cutub? Jawaab: Cabbirka wax soo saarka isdhaafka ah ee laba vectors unug wuxuu la mid yahay sine-ka xagasha u dhaxaysa. Qiimaha ugu badan waa 1 marka vectors-ku ay toosan yihiin, ugu yaraana waa 0 marka vectors-ku ay barbar socdaan.
9. Maxay tahay sababta natiijada dhibcaha ee laba vectors-ka cutubku ay u bixiyaan cosine-ka xagasha u dhaxaysa? Jawaab: Qaaciddada wax soo saarka dhibcaha ee laba vectors waxaa lagu bixiyaa natiijada cabbirkooda iyo cosine-ka xagasha u dhaxaysa. Marka labada vectors ay yihiin vectors halbeeg, cabbirkoodu waa 1, markaa wax soo saarka dhibcaha wuxuu u fududeeyaa oo keliya cosine-ka xagasha.

10. Sidee fikradda vektor cutub loogu fidiyaa nidaamyada isku-dubaridka aan ahayn Kartesian? Jawaab : Nidaamyada isku-dubaridka aan ahayn Kartesian, sida isku-dubaridka wareegsan ama dhululubada, waxaa jira vektorro cutubyo kala duwan oo u dhigma jihada isku-dubaridka kasta. Tusaale ahaan, isku-dubaridka wareegsan, vektorro cutubyadu waa r (jihada radial), θ (jihada xagasha polar), iyo φ (jihada azimuthal).