Determine the magnitude and location of the resultant of the force systems shown

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Chapter1: Units, Trigonometry. And Vectors
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Determine the magnitude and location of the resultant of the force systems shown 

The diagram provided illustrates a three-dimensional Cartesian coordinate system with forces acting on it. The coordinate system consists of the x, y, and z axes. Here's a detailed explanation of the forces and distances depicted:

1. **Axes Orientation:**
   - The x-axis extends horizontally.
   - The y-axis extends vertically.
   - The z-axis extends into the plane, angled towards the lower left.

2. **Forces:**
   - A force of **10 N** (Newtons) is acting vertically upwards along the y-axis.
   - A force of **40 N** is acting vertically downwards, located at a position **2 meters** along the z-axis and **2 meters** along the x-axis from the origin.
   - A force of **20 N** is acting vertically downwards, located **1 meter** along the x-axis and **4 meters** along the z-axis from the origin.

3. **Distances:**
   - From the origin to the point where the **40 N** force acts, there is a distance of **2 meters** along the z-axis and **2 meters** along the x-axis.
   - From the origin to the point where the **20 N** force acts, there is a distance of **1 meter** along the x-axis and **4 meters** along the z-axis.
   - The vertical distance from the origin to the placement of the **10 N** force is not explicitly measured as it is aligned along the y-axis at the point of origin.

This diagram is commonly used in physics and engineering studies to illustrate concepts such as force vectors, moments, and equilibrium in three-dimensional spaces.
Transcribed Image Text:The diagram provided illustrates a three-dimensional Cartesian coordinate system with forces acting on it. The coordinate system consists of the x, y, and z axes. Here's a detailed explanation of the forces and distances depicted: 1. **Axes Orientation:** - The x-axis extends horizontally. - The y-axis extends vertically. - The z-axis extends into the plane, angled towards the lower left. 2. **Forces:** - A force of **10 N** (Newtons) is acting vertically upwards along the y-axis. - A force of **40 N** is acting vertically downwards, located at a position **2 meters** along the z-axis and **2 meters** along the x-axis from the origin. - A force of **20 N** is acting vertically downwards, located **1 meter** along the x-axis and **4 meters** along the z-axis from the origin. 3. **Distances:** - From the origin to the point where the **40 N** force acts, there is a distance of **2 meters** along the z-axis and **2 meters** along the x-axis. - From the origin to the point where the **20 N** force acts, there is a distance of **1 meter** along the x-axis and **4 meters** along the z-axis. - The vertical distance from the origin to the placement of the **10 N** force is not explicitly measured as it is aligned along the y-axis at the point of origin. This diagram is commonly used in physics and engineering studies to illustrate concepts such as force vectors, moments, and equilibrium in three-dimensional spaces.
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