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Given below are the (x,y,z) coordinates of four points. (The units are feet) Point A: [16, 38, 12] Point B: [37, 0, 30] Point C: [0, 30, 24] Point D: [32, 0, 0] A force (vector) Fc is applied at point C. its line of action passes through point A and the direction of the force is towards point A (from point C). The magnitude of the force is 150lb

Given below are the (x,y,z) coordinates of four points. (The units are feet) Point A: [16, 38, 12] Point B: [37, 0, 30] Point C: [0, 30, 24] Point D: [32, 0, 0] A force (vector) Fc is applied at point C. its line of action passes through point A and the direction of the force is towards point A (from point C). The magnitude of the force is 150lb

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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**Title: Analyzing Force and Vectors in Cartesian Coordinates** **Introduction:** Given below are the (x,y,z) coordinates of four points, measured in feet: - **Point A:** (16, 38, 12) - **Point B:** (37, 0, 30) - **Point C:** (0, 30, 24) - **Point D:** (32, 0, 0) A force \( \vec{F_C} \) is applied at point C. Its line of action passes through point A, and the direction of the force is towards point A (from point C). The magnitude of the force is 150 lbs. Here are the steps to resolve the problem: 1. **Determine the (x, y, z) Components of the Force \( \vec{F_C} \)**: Calculate and express \( \vec{F_C} \) in Cartesian component form. 2. **Determine the Position Vector \( \vec{r_{C/D}} \)**: Find the vector \( \vec{D/C} \), which defines the location of point C relative to point D. 3. **Compute the Vector \( \vec{M_D^{F_C}} \)**: Determine the moment applied at point D due to the force \( \vec{F_C} \). 4. **Compute the Vector \( \hat{D_{DB}} \)**: Find the unit vector pointing from point D towards point B. 5. **Compute \( M_{DB}^{F_C} \)**: Calculate the moment about the line (axis) DB due to the force \( \vec{F_C} \). This result will be a scalar. 6. **Determine the Angles \( (\theta_x, \theta_y, \theta_z) \)**: Find the angles such that the components of the unit vector \( \vec{\hat{D_{DA}}} \) (pointing from point D towards point A) align with the positive (x, y, z) coordinate axes, respectively. **Graphs and Diagrams:** - **Vector Components and Position Vectors:** A diagram illustrating points A, B, C, and D in a 3D Cartesian coordinate system. The force vector \( \vec{F_C} \) should be drawn from point C towards point A. - **Moments and Unit Vectors
Transcribed Image Text:**Title: Analyzing Force and Vectors in Cartesian Coordinates** **Introduction:** Given below are the (x,y,z) coordinates of four points, measured in feet: - **Point A:** (16, 38, 12) - **Point B:** (37, 0, 30) - **Point C:** (0, 30, 24) - **Point D:** (32, 0, 0) A force \( \vec{F_C} \) is applied at point C. Its line of action passes through point A, and the direction of the force is towards point A (from point C). The magnitude of the force is 150 lbs. Here are the steps to resolve the problem: 1. **Determine the (x, y, z) Components of the Force \( \vec{F_C} \)**: Calculate and express \( \vec{F_C} \) in Cartesian component form. 2. **Determine the Position Vector \( \vec{r_{C/D}} \)**: Find the vector \( \vec{D/C} \), which defines the location of point C relative to point D. 3. **Compute the Vector \( \vec{M_D^{F_C}} \)**: Determine the moment applied at point D due to the force \( \vec{F_C} \). 4. **Compute the Vector \( \hat{D_{DB}} \)**: Find the unit vector pointing from point D towards point B. 5. **Compute \( M_{DB}^{F_C} \)**: Calculate the moment about the line (axis) DB due to the force \( \vec{F_C} \). This result will be a scalar. 6. **Determine the Angles \( (\theta_x, \theta_y, \theta_z) \)**: Find the angles such that the components of the unit vector \( \vec{\hat{D_{DA}}} \) (pointing from point D towards point A) align with the positive (x, y, z) coordinate axes, respectively. **Graphs and Diagrams:** - **Vector Components and Position Vectors:** A diagram illustrating points A, B, C, and D in a 3D Cartesian coordinate system. The force vector \( \vec{F_C} \) should be drawn from point C towards point A. - **Moments and Unit Vectors
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