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

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)
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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**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.
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