Su'aalo iyo Doodo Tusaale ah oo ku saabsan Ku darista Laba Vektor iyadoo la adeegsanayo Habka Saddexagalka ah
Pendahuluan
Vektor waa tiro leh baaxad iyo jiho labadaba. Fiisikiska iyo xisaabta, fahamka sida loogu daro laba vektor waa lama huraan si loo xalliyo dhibaatooyin kala duwan. Waxaa jira dhowr hab oo lagu daro vektor, mid ka mid ah waa habka saddexagalka. Maqaalkan, waxaan ka hadli doonnaa tusaalooyin waxaanan ka wada hadli doonnaa ku darista laba vektor iyadoo la adeegsanayo habka saddexagalka si faahfaahsan.
Habka Saddex-xagalka ee Ku-darka Vektorka
Kahor inta aynaan guda gelin dhibaatada tusaalaha ah, marka hore aan fahamno sida habka saddexagalka loo isticmaalo in lagu daro laba vector. Habka saddexagalka wuxuu ku lug leeyahay tallaabooyinka soo socda:
1. Dhigista Laba Vektor Bar Caadi ah: Vektorka ugu horreeya waxaa la dhigayaa si dabada (barta laga bilaabayo) ay ugu dhacdo barta laga bilaabayo ee la doortay.
2. Sharaxaadda Vektorka Labaad: Vektorka labaad waxaa lagu daraa dhammaadka (barta dhammaadka) ee vektorka koowaad.
3. Go'aaminta Vektorka Natiijada: Vektorka natiijada keenaya waa vektorka isku xira barta bilowga ee vektorka koowaad ilaa barta dhammaadka vektorka labaad.
Qoraalka Vektorka
Ujeeddooyinka maqaalkan awgeed, waxaan u isticmaali doonnaa calaamadaynta vector sida soo socota:
– Vektorrada ku qoran farta madow ama fallaar xagga sare ah (tusaale ahaan, A ama \(\vec{A}\)).
– Qaybaha vektor-ka ee tilmaamaha \(x\) iyo \(y\) waxaa lagu qoray qaabka \(A_x\) iyo \(A_y\) ee vektor-ka \(\vec{A}\).
Tusaalaha dhibaatooyinka
Hadda, aan eegno tusaale dhibaato ah oo naga caawin doonta inaan fahanno ku darista laba vectors iyadoo la adeegsanayo habka saddexagalka.
Su'aal:
Marka la eego laba vectors A iyo B sida soo socota:
– Vektor A wuxuu leeyahay cabbir dhan 4 cutub iyo jiho dhan 30 darajo ah oo u socota waqooyi-bari.
– Vektor B wuxuu leeyahay cabbir dhan 3 cutub iyo jiho dhan 60 darajo ah oo u socota waqooyi-bari.
Go'aami vektor-ka natiijada R laga bilaabo ku darista labada vektor iyadoo la adeegsanayo habka saddexagalka.
Dood
Tallaabada 1: Sawiridda Vektorrada
Marka hore, waxaan sawirnaa vektor A oo leh cabbir dhan 4 cutub iyo jiha dhan 30 darajo oo dhanka waqooyi-bari ah. Kadib, laga bilaabo dhammaadka vektor A, waxaan sawirnaa vektor B oo leh cabbir dhan 3 cutub iyo jiha dhan 60 darajo oo dhanka waqooyi-bari ah.
Tallaabada 2: Xisaabinta Qaybaha Vektor-ka
Marka xigta, waxaan xisaabinaynaa qaybaha vektor kasta ee jihooyinka \(x\) iyo \(y\).
Qaybaha vektorka \(\vec{A}\):
\[
A_x = A \cos \theta_1 = 4 \cos 30^\circ = 4 \jeer \frac{\sqrt{3}}{2} = 2\sqrt{3}
\]
\[
A_y = A \sin \theta_1 = 4 \sin 30^\circ = 4 \jeer \frac{1}{2} = 2
\]
Qaybaha vektorka \(\vec{B}\):
\[
B_x = B \cos \theta_2 = 3 \cos 60^\circ = 3 \jeer \frac{1}{2} = 1.5
\]
\[
B_y = B \sin \theta_2 = 3 \sin 60^\circ = 3 \ times \frac{\sqrt{3}}{2} = 1.5\sqrt{3}
\]
Tallaabada 3: Ku darista Qaybaha Vektor-ka
Waxaan ku darnaa qaybaha labada vector si aan u helno qaybaha vector-ka natiijada leh \(\vec{R}\).
\[
R_x = A_x + B_x = 2\sqrt{3} + 1.5
\]
\[
R_y = A_y + B_y = 2 + 1.5\sqrt{3}
\]
Tallaabada 4: Xisaabi Weynaanta iyo Jihada Vektor-ka Natiijada leh
Cabbirka vektor-ka natiijada leh \(\vec{R}\) waxaa lagu xisaabiyaa iyadoo la adeegsanayo aragtida Pythagorean:
\[
R = \sqrt{R_x^2 + R_y^2}
\]
\[
R_x = 2\sqrt{3} + 1.5 \qiyaastii 3.464 + 1.5 = 4.964
\]
\[
R_y = 2 + 1.5\sqrt{3} \qiyaastii 2 + 2.598 = 4.598
\]
\[
R = \sqrt{(4.964)^2 + (4.598)^2} \sqrt{24.640 + 21.145} \sqrt{45.785} \sqrt{cutubyo}
\]
Jihada vektor-ka natiijada leh \(\vec{R}\) waxaa lagu xisaabiyaa iyadoo la adeegsanayo tangent-ka shaqada trigonometric:
\[
\tan \phi = \frac{R_y}{R_x} = \frac{4.598}{4.964} \qiyaastii 0.926
\]
\[
\phi = \tan^{-1}(0.926) \qiyaastii 42.6^\circ \text{ laga bilaabo waqooyi-bari}
\]
Gabagabo
Natiijooyinka kor ku xusan, waxaan ku soo gabagabeyn karnaa in vektorka ka dhashay \(\vec{R}\) ee ka yimid ku darista vektorrada \(\vec{A}\) iyo \(\vec{B}\) iyadoo la adeegsanayo habka saddexagalka uu leeyahay cabbir qiyaas ahaan 6.75 cutub iyo jiho 42.6 darajo ah oo laga soo bilaabo waqooyi-bari.
Xiritaanka
Ku darista laba vectors iyadoo la adeegsanayo habka saddexagalka waa farsamo aad waxtar u leh oo inta badan loo isticmaalo fiisigiska iyo injineernimada. Marka aan sawirno vectors-ka oo aan ku darno qaybahooda, si fudud ayaan u heli karnaa vector-ka ka dhasha. Waxaan rajeyneynaa in maqaalkani uu kaa caawiyay inaad fahamto fikradda ku darista vector-ka iyadoo la adeegsanayo habka saddexagalka waxaana loo adeegsan karaa dhibaatooyin kala duwan oo aad kala kulanto daraasadahaaga.
