Consider the points A (10, 9) and B (0, – 7). Find the vector AB. АВ
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:**
Consider the points \( A = (10, 9) \) and \( B = (0, -7) \). Find the vector \( \vec{AB} \).
\[ \vec{AB} = \, \underline{\qquad\qquad} \]
**Solution Steps:**
To find the vector \( \vec{AB} \), we subtract the coordinates of point \( A \) from the coordinates of point \( B \).
Given:
- \( A = (10, 9) \)
- \( B = (0, -7) \)
The formula for the vector \( \vec{AB} \) is:
\[ \vec{AB} = (x_2 - x_1, y_2 - y_1) \]
Substituting the given points:
\[ \vec{AB} = (0 - 10, -7 - 9) \]
Calculating each component:
- \( x \)-component: \( 0 - 10 = -10 \)
- \( y \)-component: \( -7 - 9 = -16 \)
Therefore, the vector \( \vec{AB} \) is:
\[ \vec{AB} = (-10, -16) \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F70224edc-49fe-4fc4-bb2a-6cba35fc14ef%2F65e9ad54-e9db-4d43-b177-f86f933beb61%2F8xmcsnl_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Consider the points \( A = (10, 9) \) and \( B = (0, -7) \). Find the vector \( \vec{AB} \).
\[ \vec{AB} = \, \underline{\qquad\qquad} \]
**Solution Steps:**
To find the vector \( \vec{AB} \), we subtract the coordinates of point \( A \) from the coordinates of point \( B \).
Given:
- \( A = (10, 9) \)
- \( B = (0, -7) \)
The formula for the vector \( \vec{AB} \) is:
\[ \vec{AB} = (x_2 - x_1, y_2 - y_1) \]
Substituting the given points:
\[ \vec{AB} = (0 - 10, -7 - 9) \]
Calculating each component:
- \( x \)-component: \( 0 - 10 = -10 \)
- \( y \)-component: \( -7 - 9 = -16 \)
Therefore, the vector \( \vec{AB} \) is:
\[ \vec{AB} = (-10, -16) \]
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