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the space curve (t) = (2t, t², 2t)

the space curve (t) = (2t, t², 2t)

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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The space curve is defined by the vector function \(\vec{r}(t) = \langle 2t, t^2, 2t \rangle\). This function describes a curve in three-dimensional space where: - The x-component is \(2t\), - The y-component is \(t^2\), - The z-component is \(2t\). This curve traces a path as the parameter \(t\) varies.
Transcribed Image Text:The space curve is defined by the vector function \(\vec{r}(t) = \langle 2t, t^2, 2t \rangle\). This function describes a curve in three-dimensional space where: - The x-component is \(2t\), - The y-component is \(t^2\), - The z-component is \(2t\). This curve traces a path as the parameter \(t\) varies.
At the point (2, 1, 2), draw the vectors \(\vec{T}(1)\), \(\vec{N}(1)\), \(\vec{B}(1)\).
Transcribed Image Text:At the point (2, 1, 2), draw the vectors \(\vec{T}(1)\), \(\vec{N}(1)\), \(\vec{B}(1)\).
Expert Solution
Step 1 evaluating the unit tangent vector and unit normal vector at t=1

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