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We begin with Direction A. (a) What is the x coordinate of the vector tail (x₁)? (b) What is the x coordinate of the vector head (x₂)? (c) What is the y coordinate of the vector tail (y₁1)?

We begin with Direction A. (a) What is the x coordinate of the vector tail (x₁)? (b) What is the x coordinate of the vector head (x₂)? (c) What is the y coordinate of the vector tail (y₁1)?

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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Also what are the indicies for direction A

**Vector Coordinate Questionnaire** We begin with Direction A. (a) What is the x coordinate of the vector tail (\(x_1\))? (b) What is the x coordinate of the vector head (\(x_2\))? (c) What is the y coordinate of the vector tail (\(y_1\))? (d) What is the y coordinate of the vector head (\(y_2\))? (e) What is the z coordinate of the vector tail (\(z_1\))? (f) What is the z coordinate of the vector head (\(z_2\))? Fractional entries should be expressed in decimal form. **Answer Fields:** - (a) [Information Icon] [Entry field] [Alert Icon] \(a\) - (b) [Information Icon] [Entry field] [Alert Icon] \(a\) - (c) [Information Icon] [Entry field] \(b\) - (d) [Information Icon] [Entry field] \(b\) - (e) [Information Icon] [Entry field] \(c\) - (f) [Information Icon] [Entry field] \(c\)
Transcribed Image Text:**Vector Coordinate Questionnaire** We begin with Direction A. (a) What is the x coordinate of the vector tail (\(x_1\))? (b) What is the x coordinate of the vector head (\(x_2\))? (c) What is the y coordinate of the vector tail (\(y_1\))? (d) What is the y coordinate of the vector head (\(y_2\))? (e) What is the z coordinate of the vector tail (\(z_1\))? (f) What is the z coordinate of the vector head (\(z_2\))? Fractional entries should be expressed in decimal form. **Answer Fields:** - (a) [Information Icon] [Entry field] [Alert Icon] \(a\) - (b) [Information Icon] [Entry field] [Alert Icon] \(a\) - (c) [Information Icon] [Entry field] \(b\) - (d) [Information Icon] [Entry field] \(b\) - (e) [Information Icon] [Entry field] \(c\) - (f) [Information Icon] [Entry field] \(c\)
**Title: Understanding Direction Indices in a Cubic Unit Cell** **Instruction:** Determine the indices for the directions shown in the following cubic unit cell. **Diagram Explanation:** The image presents a three-dimensional diagram of a cubic unit cell. This diagram includes several labeled vectors within the cube, each representing a specific direction that needs to be indexed. The cube is aligned with a coordinate system where the axes are labeled as +x, +y, and +z. **Vectors and Labels:** - **Vector A:** Depicted as a solid green line running from the origin to a point on the top face of the cube. It illustrates a direction parallel to the z-axis. - **Vector B:** Shown as an orange line from the origin to a point on the front face. This direction has components along the y and z axes. - **Vector C:** A blue line extends from the origin towards the middle-left side of the top face, showing a direction inclined towards both the y and z axes. - **Vector D:** A pink line from the center of the base diagonal of the cube, indicating a balanced direction along the x, y, and z axes. **Coordinates:** - Points are marked with fractional coordinates along the edges. For instance, the vectors intersect coordinates like \( \frac{1}{2} \) on different axes representing a proportional part of the cube's dimensions. **Background Information:** In crystallography, the indices of directions in a unit cell are determined using the Miller index notation, important for defining the orientation of atomic planes and directions. Each direction is expressed in terms of a set of integers derived from the vector components along the axes of the unit cell. Understanding these directional indices is crucial for comprehending the geometric and crystallographic properties of materials in solid-state physics and materials science.
Transcribed Image Text:**Title: Understanding Direction Indices in a Cubic Unit Cell** **Instruction:** Determine the indices for the directions shown in the following cubic unit cell. **Diagram Explanation:** The image presents a three-dimensional diagram of a cubic unit cell. This diagram includes several labeled vectors within the cube, each representing a specific direction that needs to be indexed. The cube is aligned with a coordinate system where the axes are labeled as +x, +y, and +z. **Vectors and Labels:** - **Vector A:** Depicted as a solid green line running from the origin to a point on the top face of the cube. It illustrates a direction parallel to the z-axis. - **Vector B:** Shown as an orange line from the origin to a point on the front face. This direction has components along the y and z axes. - **Vector C:** A blue line extends from the origin towards the middle-left side of the top face, showing a direction inclined towards both the y and z axes. - **Vector D:** A pink line from the center of the base diagonal of the cube, indicating a balanced direction along the x, y, and z axes. **Coordinates:** - Points are marked with fractional coordinates along the edges. For instance, the vectors intersect coordinates like \( \frac{1}{2} \) on different axes representing a proportional part of the cube's dimensions. **Background Information:** In crystallography, the indices of directions in a unit cell are determined using the Miller index notation, important for defining the orientation of atomic planes and directions. Each direction is expressed in terms of a set of integers derived from the vector components along the axes of the unit cell. Understanding these directional indices is crucial for comprehending the geometric and crystallographic properties of materials in solid-state physics and materials science.
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