12.2-bo'lim: Chiziqlar tenglamalari

1 va 2 masalalar uchun chiziq tenglamasini vektor, parametrik va simmetrik shaklda bering.

1. \(\left( {2, - 4,1} \right)\) va \(\left( {0,4, - 10} \right)\) nuqtalari orqali chiziq. Yechim
2. \(\left( { - 7,2,4} \right)\) nuqtasi orqali va \(x = 5 - 8t\), \(y = 6 + t\), \(z = - 12t\) tomonidan berilgan chiziqqa parallel chiziq. Yechim
3. \(\left( {2,0,9} \right)\) va \(\left( { - 4,1, - 5} \right)\) nuqtalari orasidagi chiziq \(\vec r\left( t \right) = \left\langle {5,1 - 9t, - 8 - 4t} \right\rangle \) tomonidan berilgan chiziqqa parallelmi, ortogonalmi yoki birortasi ham emasmi? Yechim

4 va 5 masalalar uchun ikkita chiziqning kesishish nuqtasini aniqlang yoki ularning kesishmasligini ko'rsating.

1. \(x = 8 + t\), \(y = 5 + 6t\), \(z = 4 - 2t\) tomonidan berilgan chiziq va \(\vec r\left( t \right) = \left\langle { - 7 + 12t,3 - t,14 + 8t} \right\rangle \) tomonidan berilgan chiziq. Yechim
2. \(\left( {1, - 2,13} \right)\) va \(\left( {2,0, - 5} \right)\) nuqtalaridan o'tuvchi chiziq va \(\vec r\left( t \right) = \left\langle {2 + 4t, - 1 - t,3} \right\rangle \) tomonidan berilgan chiziq. Yechim
3. \(x = 9 + 21t\), \(y = - 7\), \(z = 12 - 11t\) tomonidan berilgan chiziq xy tekislik bilan kesishadimi? Agar shunday bo'lsa, fikrni bering. Yechim
4. \(x = 9 + 21t\), \(y = - 7\), \(z = 12 - 11t\) tomonidan berilgan chiziq xz tekislik bilan kesishadimi? Agar shunday bo'lsa, fikrni bering. Yechim