Tangent vector, Tangent Line, and Angle between 2 curves Let 7′(t) = (–2t – 4, −5e³t, 3e¹). Find the line (L) tangent to r(t) at t = −1. L: (x, y, z) = Question Help: Video Submit Question +t
Tangent vector, Tangent Line, and Angle between 2 curves Let 7′(t) = (–2t – 4, −5e³t, 3e¹). Find the line (L) tangent to r(t) at t = −1. L: (x, y, z) = Question Help: Video Submit Question +t
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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![**Problem Statement: Tangent Vector, Tangent Line, and Angle between 2 Curves**
Given the vector function:
\[ \vec{r}(t) = \langle -2t - 4, -5e^{5t}, 3e^{4t} \rangle \]
Find the line \( L \) tangent to \( \vec{r}(t) \) at \( t = -1 \).
The equation for the tangent line \( L \) is:
\[ L : \langle x, y, z \rangle = \langle \text{initial point} \rangle + t \langle \text{direction vector} \rangle \]
You need to fill in the expression for \( L \).
**Supporting Materials:**
- **Question Help:** [Video] (Clickable link to video resource)
- **Submit Button:** Click "Submit Question" to submit your answer.
This problem requires understanding of how to find and work with tangent vectors for parametric or vector-valued functions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8a3f3121-07ef-4e2d-8122-d3ccd0e5a601%2F3ca6cc74-820d-46fe-a0f9-36bb5bed19e6%2Flinem2q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement: Tangent Vector, Tangent Line, and Angle between 2 Curves**
Given the vector function:
\[ \vec{r}(t) = \langle -2t - 4, -5e^{5t}, 3e^{4t} \rangle \]
Find the line \( L \) tangent to \( \vec{r}(t) \) at \( t = -1 \).
The equation for the tangent line \( L \) is:
\[ L : \langle x, y, z \rangle = \langle \text{initial point} \rangle + t \langle \text{direction vector} \rangle \]
You need to fill in the expression for \( L \).
**Supporting Materials:**
- **Question Help:** [Video] (Clickable link to video resource)
- **Submit Button:** Click "Submit Question" to submit your answer.
This problem requires understanding of how to find and work with tangent vectors for parametric or vector-valued functions.
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