Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Component Form and Magnitude of Vectors**
To calculate the component form of vector \(\overrightarrow{AB}\), and to find its magnitude \(|AB|\) algebraically, follow these steps.
### Problem 3:
Given points:
- \( A(-2, -1) \)
- \( B(6, -2) \)
1. **Component Form**:
\[
\overrightarrow{AB} = (x_2 - x_1, y_2 - y_1) = (6 - (-2), -2 - (-1)) = (8, -1)
\]
2. **Magnitude**:
\[
|AB| = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(6 - (-2))^2 + (-2 - (-1))^2}
\]
\[
|AB| = \sqrt{8^2 + (-1)^2} = \sqrt{64 + 1} = \sqrt{65}
\]
### Problem 4:
Given points:
- \( A(8, 6) \)
- \( B(-4, 11) \)
1. **Component Form**:
\[
\overrightarrow{AB} = (x_2 - x_1, y_2 - y_1) = (-4 - 8, 11 - 6) = (-12, 5)
\]
2. **Magnitude**:
\[
|AB| = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(-4 - 8)^2 + (11 - 6)^2}
\]
\[
|AB| = \sqrt{(-12)^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13
\]
Use these calculations to comprehend the component form and magnitude of vectors in a coordinate plane.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F82bca876-d924-4ca0-ac20-dcea47267f8e%2Fb7be9324-1589-417d-8a01-6c664b8d9564%2Fjj2lkz_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Component Form and Magnitude of Vectors**
To calculate the component form of vector \(\overrightarrow{AB}\), and to find its magnitude \(|AB|\) algebraically, follow these steps.
### Problem 3:
Given points:
- \( A(-2, -1) \)
- \( B(6, -2) \)
1. **Component Form**:
\[
\overrightarrow{AB} = (x_2 - x_1, y_2 - y_1) = (6 - (-2), -2 - (-1)) = (8, -1)
\]
2. **Magnitude**:
\[
|AB| = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(6 - (-2))^2 + (-2 - (-1))^2}
\]
\[
|AB| = \sqrt{8^2 + (-1)^2} = \sqrt{64 + 1} = \sqrt{65}
\]
### Problem 4:
Given points:
- \( A(8, 6) \)
- \( B(-4, 11) \)
1. **Component Form**:
\[
\overrightarrow{AB} = (x_2 - x_1, y_2 - y_1) = (-4 - 8, 11 - 6) = (-12, 5)
\]
2. **Magnitude**:
\[
|AB| = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(-4 - 8)^2 + (11 - 6)^2}
\]
\[
|AB| = \sqrt{(-12)^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13
\]
Use these calculations to comprehend the component form and magnitude of vectors in a coordinate plane.
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