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1. Determine the angle e Ę Cin.degreces) that the force F makes with the postive Z axis. 2. Determine the unit vector Kp which acts in the direction of the Force F.

1. Determine the angle e Ę Cin.degreces) that the force F makes with the postive Z axis. 2. Determine the unit vector Kp which acts in the direction of the Force F.

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### Educational Explanation of the Diagram #### Description The diagram represents a three-dimensional Cartesian coordinate system with forces acting at point \( O \). The coordinate axes are labeled as \( x \), \( y \), and \( z \) in meters, and the directions are specified with unit vectors \( \hat{i} \), \( \hat{j} \), and \( \hat{k} \) representing the \( x \)-, \( y \)-, and \( z \)-axes respectively. #### Diagram Elements 1. **Axes**: - The \( x \)-axis extends horizontally and is denoted as +\( \hat{i} \). - The \( y \)-axis extends horizontally to the right and is denoted as +\( \hat{j} \). - The \( z \)-axis extends vertically and is denoted as +\( \hat{k} \). 2. **Forces**: - There is a force of 600 N acting downward along the \( z \)-axis from point \( O \). - A force of 400 N is acting along the \( y \)-axis, 45° above the horizontal plane from point \( O \). 3. **Point \( A \)**: - Point \( A \) is located at coordinates \((-1, -3, +3)\) meters. 4. **Angles**: - There is an angle of 60° between the negative \( x \)-axis and some vector extending from point \( O \). - The 45° angle is indicated between upward direction and the force vector \( F \). 5. **Dimensions**: - A vertical dashed line extends 3 meters upward. - A horizontal dashed line extends 1 meter to the left and 3 meters to the right. #### Coordinate Representation - **Point A Coordinates ( \( x, y, z \) )**: - \( x = -1 \) meters - \( y = -3 \) meters - \( z = +3 \) meters #### Analytical Context The diagram can be used to analyze vectors in three-dimensional space, specifically focusing on identifying the resultant forces and angles in mechanical systems. It helps understand how forces interact in a 3D-coordinated structure, and how they can be resolved into components along x, y, and z-axes. This type of analysis is crucial in fields such
Transcribed Image Text:### Educational Explanation of the Diagram #### Description The diagram represents a three-dimensional Cartesian coordinate system with forces acting at point \( O \). The coordinate axes are labeled as \( x \), \( y \), and \( z \) in meters, and the directions are specified with unit vectors \( \hat{i} \), \( \hat{j} \), and \( \hat{k} \) representing the \( x \)-, \( y \)-, and \( z \)-axes respectively. #### Diagram Elements 1. **Axes**: - The \( x \)-axis extends horizontally and is denoted as +\( \hat{i} \). - The \( y \)-axis extends horizontally to the right and is denoted as +\( \hat{j} \). - The \( z \)-axis extends vertically and is denoted as +\( \hat{k} \). 2. **Forces**: - There is a force of 600 N acting downward along the \( z \)-axis from point \( O \). - A force of 400 N is acting along the \( y \)-axis, 45° above the horizontal plane from point \( O \). 3. **Point \( A \)**: - Point \( A \) is located at coordinates \((-1, -3, +3)\) meters. 4. **Angles**: - There is an angle of 60° between the negative \( x \)-axis and some vector extending from point \( O \). - The 45° angle is indicated between upward direction and the force vector \( F \). 5. **Dimensions**: - A vertical dashed line extends 3 meters upward. - A horizontal dashed line extends 1 meter to the left and 3 meters to the right. #### Coordinate Representation - **Point A Coordinates ( \( x, y, z \) )**: - \( x = -1 \) meters - \( y = -3 \) meters - \( z = +3 \) meters #### Analytical Context The diagram can be used to analyze vectors in three-dimensional space, specifically focusing on identifying the resultant forces and angles in mechanical systems. It helps understand how forces interact in a 3D-coordinated structure, and how they can be resolved into components along x, y, and z-axes. This type of analysis is crucial in fields such
### Physics Problem Set **Problem 1:** Determine the angle \(\theta^F_z\) (in degrees) that the force \(\vec{F}\) makes with the positive \(z\) axis. **Problem 2:** Determine the unit vector \(\hat{r}_F\) which acts in the direction of the force \(\vec{F}\). #### Details: 1. **Angle Calculation:** - Symbol: \(\theta^F_z\) - Description: This is the angle between the force vector \(\vec{F}\) and the positive \(z\) axis. 2. **Unit Vector Calculation:** - Symbol: \(\hat{r}_F\) - Description: This is the unit vector that points in the direction of the force vector \(\vec{F}\). Note: When solving these problems, ensure to apply the fundamental concepts of vector analysis and trigonometry. For the angle determination, use the dot product of vectors, and for the unit vector, normalize the force vector by dividing it by its magnitude.
Transcribed Image Text:### Physics Problem Set **Problem 1:** Determine the angle \(\theta^F_z\) (in degrees) that the force \(\vec{F}\) makes with the positive \(z\) axis. **Problem 2:** Determine the unit vector \(\hat{r}_F\) which acts in the direction of the force \(\vec{F}\). #### Details: 1. **Angle Calculation:** - Symbol: \(\theta^F_z\) - Description: This is the angle between the force vector \(\vec{F}\) and the positive \(z\) axis. 2. **Unit Vector Calculation:** - Symbol: \(\hat{r}_F\) - Description: This is the unit vector that points in the direction of the force vector \(\vec{F}\). Note: When solving these problems, ensure to apply the fundamental concepts of vector analysis and trigonometry. For the angle determination, use the dot product of vectors, and for the unit vector, normalize the force vector by dividing it by its magnitude.
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