Example 2-3-8 - Maple Help



Chapter 2: Space Curves



Section 2.3: Tangent Vectors



Example 2.3.8



If $\mathbf{R}\left(p\right)$ is the position-vector form of the curve $C$ defined parametrically by the equations , $p\in \left[0,\mathrm{π}\right]$,

 a) Obtain $\mathbf{R}\prime \left(p\right),\mathrm{ρ}\left(p\right)$ and $\mathbf{T}\left(p\right)$, where $\mathrm{ρ}=∥\mathbf{R}\prime ∥$ and $\mathbf{T}=\mathbf{R}\prime /\mathrm{ρ}$.
 b) Graph $C$ and the vectors $\mathbf{T}\left(0\right),\mathbf{T}\left(1\right),\mathbf{T}\left(2\right)$.
 c) On the given interval, graph $\mathrm{ρ}$ and determine its absolute minimum and the point on the curve where this minimum occurs.