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7. Cross and Dot Product and Resultant Distinctions Two forces act on an object A with an alignment that is orthogonal to the plane formed by the force vectors. The magnitudes of the force vectors are F₁ = 2,236 N and F₂ = 3,733 N. 2

7. Cross and Dot Product and Resultant Distinctions Two forces act on an object A with an alignment that is orthogonal to the plane formed by the force vectors. The magnitudes of the force vectors are F₁ = 2,236 N and F₂ = 3,733 N. 2

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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**Cross and Dot Product and Resultant Distinctions** Two forces act on an object A with an alignment that is orthogonal to the plane formed by the force vectors. The magnitudes of the force vectors are \( F_1 = 2,236 \) N and \( F_2 = 3,733 \) N. **Show your work:** (a) Determine the cross product and the dot product of the two force vectors. (b) Determine the resultant of the two forces and its orientation from the positive x-axis. (c) Interpret your results. --- **Explanation of Graph/Diagram:** The provided diagram is a grid plot showing the vectors \( F_1 \) and \( F_2 \) in an xy-coordinate system. - The x-axis is labeled as \( X \), and the y-axis is labeled as \( Y \). - Vector \( F_1 \) originates from the point (0, 0) (denoted as A) and extends to a point approximately at (2.0, 10.0) on the grid. - Vector \( F_2 \) also originates from the point (0, 0) and extends to a point approximately at (3.5, -3.5) on the grid. In the diagram: - Vector \( F_1 \) is represented with positive y-direction. - Vector \( F_2 \) appears to split into two components along the x and y axes: approximately (3.5) in the positive x-direction and (-4) in the negative y-direction. The grid lines and markers help in identifying the coordinates and the lengths of the vectors.
Transcribed Image Text:**Cross and Dot Product and Resultant Distinctions** Two forces act on an object A with an alignment that is orthogonal to the plane formed by the force vectors. The magnitudes of the force vectors are \( F_1 = 2,236 \) N and \( F_2 = 3,733 \) N. **Show your work:** (a) Determine the cross product and the dot product of the two force vectors. (b) Determine the resultant of the two forces and its orientation from the positive x-axis. (c) Interpret your results. --- **Explanation of Graph/Diagram:** The provided diagram is a grid plot showing the vectors \( F_1 \) and \( F_2 \) in an xy-coordinate system. - The x-axis is labeled as \( X \), and the y-axis is labeled as \( Y \). - Vector \( F_1 \) originates from the point (0, 0) (denoted as A) and extends to a point approximately at (2.0, 10.0) on the grid. - Vector \( F_2 \) also originates from the point (0, 0) and extends to a point approximately at (3.5, -3.5) on the grid. In the diagram: - Vector \( F_1 \) is represented with positive y-direction. - Vector \( F_2 \) appears to split into two components along the x and y axes: approximately (3.5) in the positive x-direction and (-4) in the negative y-direction. The grid lines and markers help in identifying the coordinates and the lengths of the vectors.
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