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Vector Math: Two forces act on the hook at A. F has already been expressed in vector notation. Show all calculations on your paper and circle final answers. Use this figure for the next 3 questions. F = {-6i+9j+ 3 k) kN A 3 m -2 m X TAO=8 KN 1 m

Vector Math: Two forces act on the hook at A. F has already been expressed in vector notation. Show all calculations on your paper and circle final answers. Use this figure for the next 3 questions. F = {-6i+9j+ 3 k) kN A 3 m -2 m X TAO=8 KN 1 m

Question
7
### Vector Math: Forces Acting on a Hook Two forces act on the hook at point A. Force \( \mathbf{F} \) has already been expressed in vector notation. Show all calculations on your paper and circle final answers. **Vector Force \( \mathbf{F} \):** \[ \mathbf{F} = \{-6 \hat{i} + 9 \hat{j} + 3 \hat{k}\} \text{kN} \] **Tension Force \( T_{AO} \):** \[ T_{AO} = 8 \text{kN} \] The following diagram depicts point A where the forces are acting: - Point A is suspended at a position (3 meters in y, 2 meters in x, 1 meter in z). - The force \( \mathbf{F} \) is applied as shown by its vector components. - The tension force \( T_{AO} \) stretches diagonally from point A to the origin O. ### Diagram Explanation: The figure provided includes a 3D coordinate system with the following labeled elements: - Point A, where the forces are applied, is located at \((2, 3, 1)\) meters in the \(x\), \(y\), and \(z\) axes, respectively. - The vector force \( \mathbf{F} \), whose component notation is \(\{-6 \hat{i} + 9 \hat{j} + 3 \hat{k}\}\) kN, represents the magnitudes along the \(x\), \(y\), and \(z\) axes. - A tension force \( T_{AO} \) of 8 kN acts from point A directly to the origin O. ### Steps to Solve: 1. **Identify the forces in vector notation**: - \( \mathbf{F} = \{-6 \hat{i} + 9 \hat{j} + 3 \hat{k}\} \text{kN} \) - \( T_{AO} = 8 \text{kN} \) 2. **Analyze the balance of forces** and solve for any unknowns: - Utilize vector addition and subtraction. - Apply principles of equilibrium, if applicable. 3. **Calculate the resultant force** and provide necessary explanations for each computation step. ### For the Next Three Questions: Use this figure to solve for:
Transcribed Image Text:### Vector Math: Forces Acting on a Hook Two forces act on the hook at point A. Force \( \mathbf{F} \) has already been expressed in vector notation. Show all calculations on your paper and circle final answers. **Vector Force \( \mathbf{F} \):** \[ \mathbf{F} = \{-6 \hat{i} + 9 \hat{j} + 3 \hat{k}\} \text{kN} \] **Tension Force \( T_{AO} \):** \[ T_{AO} = 8 \text{kN} \] The following diagram depicts point A where the forces are acting: - Point A is suspended at a position (3 meters in y, 2 meters in x, 1 meter in z). - The force \( \mathbf{F} \) is applied as shown by its vector components. - The tension force \( T_{AO} \) stretches diagonally from point A to the origin O. ### Diagram Explanation: The figure provided includes a 3D coordinate system with the following labeled elements: - Point A, where the forces are applied, is located at \((2, 3, 1)\) meters in the \(x\), \(y\), and \(z\) axes, respectively. - The vector force \( \mathbf{F} \), whose component notation is \(\{-6 \hat{i} + 9 \hat{j} + 3 \hat{k}\}\) kN, represents the magnitudes along the \(x\), \(y\), and \(z\) axes. - A tension force \( T_{AO} \) of 8 kN acts from point A directly to the origin O. ### Steps to Solve: 1. **Identify the forces in vector notation**: - \( \mathbf{F} = \{-6 \hat{i} + 9 \hat{j} + 3 \hat{k}\} \text{kN} \) - \( T_{AO} = 8 \text{kN} \) 2. **Analyze the balance of forces** and solve for any unknowns: - Utilize vector addition and subtraction. - Apply principles of equilibrium, if applicable. 3. **Calculate the resultant force** and provide necessary explanations for each computation step. ### For the Next Three Questions: Use this figure to solve for:
### Instruction for Forces Resultant Calculation **Task:** Determine the resultant of the forces \( F \) and \( T_{A0} \). Enter your answer in the blank provided. **Interface:** - **Text Editing Options:** - **Edit** - **Format** - **Table** - **Formatting Toolbar:** - Font size selection (12pt) - Paragraph settings - Bold \(\mathbf{B}\) - Italic \(\mathit{I}\) - Underline \(\underline{U}\) - Format painter \(\mathbf{A}\) - Font color - Bullets and numbering - Text alignment options (left, center, right, justify) - Line spacing --- **Note for Educators:** This task requires students to understand vector addition for forces. They should calculate the resultant force from two given forces, \( F \) and \( T_{A0} \). **Graphical Representation:** There are no specific graphs or diagrams displayed in this image. It shows a generic text editor with usual formatting options. Students should utilize these tools to input and format their answer appropriately.
Transcribed Image Text:### Instruction for Forces Resultant Calculation **Task:** Determine the resultant of the forces \( F \) and \( T_{A0} \). Enter your answer in the blank provided. **Interface:** - **Text Editing Options:** - **Edit** - **Format** - **Table** - **Formatting Toolbar:** - Font size selection (12pt) - Paragraph settings - Bold \(\mathbf{B}\) - Italic \(\mathit{I}\) - Underline \(\underline{U}\) - Format painter \(\mathbf{A}\) - Font color - Bullets and numbering - Text alignment options (left, center, right, justify) - Line spacing --- **Note for Educators:** This task requires students to understand vector addition for forces. They should calculate the resultant force from two given forces, \( F \) and \( T_{A0} \). **Graphical Representation:** There are no specific graphs or diagrams displayed in this image. It shows a generic text editor with usual formatting options. Students should utilize these tools to input and format their answer appropriately.
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