Consider the curve r= (t,1–2t²,-1-2t?), t= – 1 Find the equation of the normal plane of the curve at the given point x + 4y + 4z = – 17 x + 4y +2z = – 17 x - 4y – 4z = 17 x + 4y – 4z = 17 x - 4y + 4z = - 17 а. b. с. d. е. O a e d O b
Consider the curve r= (t,1–2t²,-1-2t?), t= – 1 Find the equation of the normal plane of the curve at the given point x + 4y + 4z = – 17 x + 4y +2z = – 17 x - 4y – 4z = 17 x + 4y – 4z = 17 x - 4y + 4z = - 17 а. b. с. d. е. O a e d O b
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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![**Curve Analysis and Normal Plane Equation**
Consider the curve defined by:
\[
\mathbf{r} = \langle t, 1 - 2t^2, -1 - 2t^2 \rangle, \quad t = -1
\]
Your task is to find the equation of the normal plane to the curve at the given point. Choose the correct option from the list below:
**Options:**
a. \( x + 4y + 4z = -17 \)
b. \( x + 4y + 2z = -17 \)
c. \( x - 4y - 4z = 17 \)
d. \( x + 4y - 4z = 17 \)
e. \( x - 4y + 4z = -17 \)
**Selection:**
- [ ] a
- [ ] c
- [ ] e
- [ ] d
- [ ] b
Choose the equation that correctly represents the normal plane of the curve at \( t = -1 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa72e8965-bd79-4464-a740-a72095a0be2c%2F60f26e33-35c7-4fba-8a6f-d036fb4ab0d5%2Fly6y1zw_processed.png&w=3840&q=75)
Transcribed Image Text:**Curve Analysis and Normal Plane Equation**
Consider the curve defined by:
\[
\mathbf{r} = \langle t, 1 - 2t^2, -1 - 2t^2 \rangle, \quad t = -1
\]
Your task is to find the equation of the normal plane to the curve at the given point. Choose the correct option from the list below:
**Options:**
a. \( x + 4y + 4z = -17 \)
b. \( x + 4y + 2z = -17 \)
c. \( x - 4y - 4z = 17 \)
d. \( x + 4y - 4z = 17 \)
e. \( x - 4y + 4z = -17 \)
**Selection:**
- [ ] a
- [ ] c
- [ ] e
- [ ] d
- [ ] b
Choose the equation that correctly represents the normal plane of the curve at \( t = -1 \).
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