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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Can anyone please help me to solve this problem? I am stuck please help me!
![**Problem Statement:**
Let \( R = (2, 1) \). Find the point \( P \) such that the vector \(\overrightarrow{PR}\) has components \(\langle -3, 1 \rangle\).
**Solution:**
To find the point \( P = (x, y) \), we need to solve for \( x \) and \( y \) given that the vector \(\overrightarrow{PR} = \langle x - 2, y - 1 \rangle\) has the components \(\langle -3, 1 \rangle\).
1. Set the components equal to each other:
\[
x - 2 = -3 \quad \text{and} \quad y - 1 = 1
\]
2. Solve for \( x \):
\[
x - 2 = -3
\]
\[
x = -3 + 2
\]
\[
x = -1
\]
3. Solve for \( y \):
\[
y - 1 = 1
\]
\[
y = 1 + 1
\]
\[
y = 2
\]
Thus, the point \( P \) is \((-1, 2)\).
**Conclusion:**
The point \( P \) such that vector \(\overrightarrow{PR}\) has components \(\langle -3, 1 \rangle\) when \( R = (2, 1) \) is \( P = (-1, 2) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F99d15f92-0bff-4b4d-a47e-2ac33d144271%2F240a2b47-1d0c-4db0-bd03-3499a78844fd%2F7r54gwd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Let \( R = (2, 1) \). Find the point \( P \) such that the vector \(\overrightarrow{PR}\) has components \(\langle -3, 1 \rangle\).
**Solution:**
To find the point \( P = (x, y) \), we need to solve for \( x \) and \( y \) given that the vector \(\overrightarrow{PR} = \langle x - 2, y - 1 \rangle\) has the components \(\langle -3, 1 \rangle\).
1. Set the components equal to each other:
\[
x - 2 = -3 \quad \text{and} \quad y - 1 = 1
\]
2. Solve for \( x \):
\[
x - 2 = -3
\]
\[
x = -3 + 2
\]
\[
x = -1
\]
3. Solve for \( y \):
\[
y - 1 = 1
\]
\[
y = 1 + 1
\]
\[
y = 2
\]
Thus, the point \( P \) is \((-1, 2)\).
**Conclusion:**
The point \( P \) such that vector \(\overrightarrow{PR}\) has components \(\langle -3, 1 \rangle\) when \( R = (2, 1) \) is \( P = (-1, 2) \).
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