Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve. r(t) = (3cos t)i + (3sin t)j + (√√3 t)k, Find the curve's unit tangent vector. T(t) = i + j + k 0≤t≤t
Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve. r(t) = (3cos t)i + (3sin t)j + (√√3 t)k, Find the curve's unit tangent vector. T(t) = i + j + k 0≤t≤t
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Also, find the length of the indicated portion of the curve.
Find Part A and B
![**Problem Statement:**
**Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.**
\[ \mathbf{r}(t) = (3\cos t)\mathbf{i} + (3\sin t)\mathbf{j} + (\sqrt{3}t)\mathbf{k}, \quad 0 \leq t \leq \pi \]
---
**Task:**
**Find the curve's unit tangent vector.**
\[ \mathbf{T}(t) = \_\_\_ \mathbf{i} + \_\_\_ \mathbf{j} + \_\_\_ \mathbf{k} \]
In this task, students are expected to find the unit tangent vector for the given parameterized curve \(\mathbf{r}(t)\). They will calculate the derivative of \(\mathbf{r}(t)\) with respect to \(t\) to find the tangent vector and then normalize it to get the unit tangent vector. Additionally, students are asked to determine the length of the specified part of the curve.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F61cb8e6c-6e45-4d89-8a08-e4b0e2f3d1e4%2Fcaf2c315-03a0-4b0d-8a35-f66ae5d1e660%2Fhq2fivlf_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
**Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.**
\[ \mathbf{r}(t) = (3\cos t)\mathbf{i} + (3\sin t)\mathbf{j} + (\sqrt{3}t)\mathbf{k}, \quad 0 \leq t \leq \pi \]
---
**Task:**
**Find the curve's unit tangent vector.**
\[ \mathbf{T}(t) = \_\_\_ \mathbf{i} + \_\_\_ \mathbf{j} + \_\_\_ \mathbf{k} \]
In this task, students are expected to find the unit tangent vector for the given parameterized curve \(\mathbf{r}(t)\). They will calculate the derivative of \(\mathbf{r}(t)\) with respect to \(t\) to find the tangent vector and then normalize it to get the unit tangent vector. Additionally, students are asked to determine the length of the specified part of the curve.
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