12.8-bo'lim: Tangent, normal va binormal vektorlar

1 va 2 masalalar uchun berilgan vektor funksiya uchun birlik tangens vektorini toping.

1. \(\vec r\left( t \right) = \left\langle {{t^2} + 1,3 - t,{t^3}} \right\rangle \) Yechim
2. \(\vec r\left( t \right) = t{{\bf{e}}^{2t}}\,\vec i + \left( {2 - {t^2}} \right)\vec j - {{\bf{e}}^{2t}}\vec k\) Yechim

3 va 4-masalalar uchun berilgan nuqtadagi vektor funksiyasiga teginish chizig‘ini toping.

1. \(\vec r\left( t \right) = \cos \left( {4t} \right)\vec i + 3\sin \left( {4t} \right)\vec j + {t^3}\vec k\) at \(t = \pi \). Yechim
2. \(\displaystyle \vec r\left( t \right) = \left\langle {7{{\bf{e}}^{2 - t}},\frac{{16}}{{{t^3}}},5 - t} \right\rangle \) at \(t = 2\). Yechim
3. Quyidagi vektor funksiya uchun normal va binormal vektor birligini toping. \(\vec r\left( t \right) = \left\langle {\cos \left( {2t} \right),\sin \left( {2t} \right),3} \right\rangle \) Yechim