15. Which is the component form of the vector shown? -2- * (1, 2) -4 (-5, -3) O (4,-7) O (7.-4)

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,...
icon
Related questions
Question
100%
**Vector Component Form Problem**

**Question 15: Which is the component form of the vector shown?**

**Graph Description:**
- The graph represents a coordinate plane with horizontal (x-axis) and vertical (y-axis) axes.
- The axes are labeled with tick marks at intervals of 1 unit, ranging from -6 to 6 on both axes.
- A vector is depicted as a directed line segment starting from the point (-5, -3) and ending at the point (1, 2).
- The initial point is marked at (-5, -3) and the terminal point is marked at (1, 2).

**Answer Options:**
- ⃗ < -6, -5 >
- ⃗ < -5, -6 >
- ⃗ < -4, -7 >
- ⃗ < 7, 4 >

**Explanation:**
The component form of a vector is given by subtracting the coordinates of the initial point from the coordinates of the terminal point. 

For vector from (-5, -3) to (1, 2):

- Subtract the x-coordinates: 1 - (-5) = 1 + 5 = 6
- Subtract the y-coordinates: 2 - (-3) = 2 + 3 = 5

Therefore, the component form of the vector is ⃗ < 6, 5 >. Note that this component form matches none of the given options, indicating an error in the provided choices.
Transcribed Image Text:**Vector Component Form Problem** **Question 15: Which is the component form of the vector shown?** **Graph Description:** - The graph represents a coordinate plane with horizontal (x-axis) and vertical (y-axis) axes. - The axes are labeled with tick marks at intervals of 1 unit, ranging from -6 to 6 on both axes. - A vector is depicted as a directed line segment starting from the point (-5, -3) and ending at the point (1, 2). - The initial point is marked at (-5, -3) and the terminal point is marked at (1, 2). **Answer Options:** - ⃗ < -6, -5 > - ⃗ < -5, -6 > - ⃗ < -4, -7 > - ⃗ < 7, 4 > **Explanation:** The component form of a vector is given by subtracting the coordinates of the initial point from the coordinates of the terminal point. For vector from (-5, -3) to (1, 2): - Subtract the x-coordinates: 1 - (-5) = 1 + 5 = 6 - Subtract the y-coordinates: 2 - (-3) = 2 + 3 = 5 Therefore, the component form of the vector is ⃗ < 6, 5 >. Note that this component form matches none of the given options, indicating an error in the provided choices.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education