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Find the T(1), Ñ(1), B(t), and K(t) of the following space curves. (a) F(t)=(3 sint)i + (3 cost)j + 4tk (b) F(t)=(e' cost)i + (e' sint)j +2k (c) F(t)=(sint)i + (√2 cost)]+(sint)

Find the T(1), Ñ(1), B(t), and K(t) of the following space curves. (a) F(t)=(3 sint)i + (3 cost)j + 4tk (b) F(t)=(e' cost)i + (e' sint)j +2k (c) F(t)=(sint)i + (√2 cost)]+(sint)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Find the \(\vec{T}(t)\), \(\vec{N}(t)\), \(\vec{B}(t)\), and \(\kappa(t)\) of the following space curves. (a) \(\vec{r}(t) = (3 \sin t) \, \vec{i} + (3 \cos t) \, \vec{j} + 4t \, \vec{k}\) (b) \(\vec{r}(t) = (e^t \cos t) \, \vec{i} + (e^t \sin t) \, \vec{j} + 2t \, \vec{k}\) (c) \(\vec{r}(t) = (\sin t) \, \vec{i} + (\sqrt{2} \cos t) \, \vec{j} + (\sin t) \, \vec{k}\)
Transcribed Image Text:Find the \(\vec{T}(t)\), \(\vec{N}(t)\), \(\vec{B}(t)\), and \(\kappa(t)\) of the following space curves. (a) \(\vec{r}(t) = (3 \sin t) \, \vec{i} + (3 \cos t) \, \vec{j} + 4t \, \vec{k}\) (b) \(\vec{r}(t) = (e^t \cos t) \, \vec{i} + (e^t \sin t) \, \vec{j} + 2t \, \vec{k}\) (c) \(\vec{r}(t) = (\sin t) \, \vec{i} + (\sqrt{2} \cos t) \, \vec{j} + (\sin t) \, \vec{k}\)
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