**Title:** Understanding Cartesian Coordinate Systems and Unit Vectors**Instructions:** Draw the missing unit vector for each of the Cartesian coordinate systems below. If the unit vector should point into or out of the board, just draw the appropriate symbol to denote those directions.---**A. Coordinate System A**- **Unit Vector \( \mathbf{i} \):** Represented by a downward arrow.- **Unit Vector \( \mathbf{j} \):** Indicated by a circle with a dot, symbolizing a vector pointing out of the board.- **Unit Vector \( \mathbf{k} \):** Missing and needs to be determined.**Symbols Explanation:**- Circle with a dot (\( \odot \)): Represents a vector coming out of the board.- Circle with a cross (\( \otimes \)): Represents a vector going into the board.---**B. Coordinate System B**- **Unit Vector \( \mathbf{i} \):** Indicated by a circle with a cross, symbolizing a vector going into the board.- **Unit Vector \( \mathbf{j} \):** Missing and needs to be determined.- **Unit Vector \( \mathbf{k} \):** Represented by an arrow pointing diagonally to the top right.---**C. Coordinate System C**- **Unit Vector \( \mathbf{i} \):** Represented by an arrow pointing diagonally to the bottom left.- **Unit Vector \( \mathbf{j} \):** Missing and needs to be determined.- **Unit Vector \( \mathbf{k} \):** Represented by an arrow pointing diagonally to the top right.**Note:** In all systems, ensure that the drawn vectors follow right-hand rule conventions for the Cartesian coordinate system. Adjust the missing vectors accordingly to maintain consistency with this rule.

The missing unit vector can be found using Left hand Rule If we stretch our thumb, middle finger and the index finger of our left hand in mutually perpendicular (making an angle of 90 degrees) directions to each other, Then middle finger gives direction of x⏞ , index finger of y⏞ and thumb of z⏞.

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Physics

Draw the missing unit vector for each of the Cartesian coordinate stems below. If the unit vector should point into or out of the board, st draw the appropriate symbol to denote those directions. A. Coordinate System A X ŷ N₂ B. Coordinate System B X 2 ŷ N₂ 2

Draw the missing unit vector for each of the Cartesian coordinate stems below. If the unit vector should point into or out of the board, st draw the appropriate symbol to denote those directions. A. Coordinate System A X ŷ N₂ B. Coordinate System B X 2 ŷ N₂ 2

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

**Title:** Understanding Cartesian Coordinate Systems and Unit Vectors

**Instructions:** Draw the missing unit vector for each of the Cartesian coordinate systems below. If the unit vector should point into or out of the board, just draw the appropriate symbol to denote those directions.

---

**A. Coordinate System A**

- **Unit Vector \( \mathbf{i} \):** Represented by a downward arrow.
- **Unit Vector \( \mathbf{j} \):** Indicated by a circle with a dot, symbolizing a vector pointing out of the board.
- **Unit Vector \( \mathbf{k} \):** Missing and needs to be determined.

**Symbols Explanation:**
- Circle with a dot (\( \odot \)): Represents a vector coming out of the board.
- Circle with a cross (\( \otimes \)): Represents a vector going into the board.

---

**B. Coordinate System B**

- **Unit Vector \( \mathbf{i} \):** Indicated by a circle with a cross, symbolizing a vector going into the board.
- **Unit Vector \( \mathbf{j} \):** Missing and needs to be determined.
- **Unit Vector \( \mathbf{k} \):** Represented by an arrow pointing diagonally to the top right.

---

**C. Coordinate System C**

- **Unit Vector \( \mathbf{i} \):** Represented by an arrow pointing diagonally to the bottom left.
- **Unit Vector \( \mathbf{j} \):** Missing and needs to be determined.
- **Unit Vector \( \mathbf{k} \):** Represented by an arrow pointing diagonally to the top right.

**Note:** In all systems, ensure that the drawn vectors follow right-hand rule conventions for the Cartesian coordinate system. Adjust the missing vectors accordingly to maintain consistency with this rule.

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