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1. If the resultant force acting on the hook is FR = -400 į + 200 j + 250 k (Įb), determine the magnitude and coordinate direction angles of F.

1. If the resultant force acting on the hook is FR = -400 į + 200 j + 250 k (Įb), determine the magnitude and coordinate direction angles of F.

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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**Problem Statement:** 1. If the resultant force acting on the hook is \( \mathbf{F}_R = -400 \, \mathbf{i} + 200 \, \mathbf{j} + 250 \, \mathbf{k} \, (\text{lb}) \), determine the magnitude and coordinate direction angles of \( \mathbf{F} \). **Diagram Explanation:** The diagram shows a three-dimensional coordinate system with axes labeled \( x \), \( y \), and \( z \) with a hook mounted on a wall. A force \( \mathbf{F} \) is represented as a vector emanating from the hook. The force vector makes angles \( \alpha \), \( \beta \), and \( \gamma \) with the \( x \), \( y \), and \( z \)-axes respectively. - A triangle is formed in the \( xy \)-plane, and one of its angles is \( 30^\circ \). - A force \( \mathbf{F}_1 = 800 \, \text{lb} \) is acting downward, forming another part of the shown system. - Dimensions of the triangle in the \( xy \)-plane are marked as 4, 3, and 5 units. **Objective:** The task is to calculate the magnitude of the force \( \mathbf{F} \) and determine its coordinate direction angles \( \alpha \), \( \beta \), and \( \gamma \) using the provided vector components.
Transcribed Image Text:**Problem Statement:** 1. If the resultant force acting on the hook is \( \mathbf{F}_R = -400 \, \mathbf{i} + 200 \, \mathbf{j} + 250 \, \mathbf{k} \, (\text{lb}) \), determine the magnitude and coordinate direction angles of \( \mathbf{F} \). **Diagram Explanation:** The diagram shows a three-dimensional coordinate system with axes labeled \( x \), \( y \), and \( z \) with a hook mounted on a wall. A force \( \mathbf{F} \) is represented as a vector emanating from the hook. The force vector makes angles \( \alpha \), \( \beta \), and \( \gamma \) with the \( x \), \( y \), and \( z \)-axes respectively. - A triangle is formed in the \( xy \)-plane, and one of its angles is \( 30^\circ \). - A force \( \mathbf{F}_1 = 800 \, \text{lb} \) is acting downward, forming another part of the shown system. - Dimensions of the triangle in the \( xy \)-plane are marked as 4, 3, and 5 units. **Objective:** The task is to calculate the magnitude of the force \( \mathbf{F} \) and determine its coordinate direction angles \( \alpha \), \( \beta \), and \( \gamma \) using the provided vector components.
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