**Guidelines for Drawing Coordinate Axes**When drawing your 2- and 3-dimensional coordinate axes, follow these instructions:1. **Labeling**: Ensure that you label the positive side of each axis clearly.2. **Tick Marks**: Include tick marks on each axis to indicate units of measurement.3. **Scaling**: Make sure each axis has a scale.For 3-dimensional coordinate systems, adhere to the **right-hand rule**:- The right-hand rule helps in determining the direction of the axes. Point your thumb, index finger, and middle finger perpendicular to each other. The thumb points in the direction of the x-axis, the index finger in the direction of the y-axis, and the middle finger in the direction of the z-axis.**Labeling Objects**: Always label all objects you graph for clarity.**Vector Notation**: Use appropriate vector notation whenever you are writing a vector to differentiate it from scalar quantities. ### Vectors and Their Graphical Representations**Vectors \( \mathbf{u} \) and \( \mathbf{v} \)**Below are graphical representations of the vectors \( \mathbf{u} \) and \( \mathbf{v} \).![Vectors \( \mathbf{u} \) and \( \mathbf{v} \)](insert_graph_image_here)**Instructions:**Provide graphs of the following vectors in the space above. Label each vector appropriately.### Vectors to be graphed:(a) **Vector \( \mathbf{a} = -\mathbf{u} \)**(b) **Vector \( \mathbf{b} = 2\mathbf{v} \)**(c) **Vector \( \mathbf{s} = \mathbf{v} + \mathbf{u} \)**(d) **Vector \( \mathbf{d} = \mathbf{v} - \mathbf{u} \)**(e) **Vector \( \mathbf{p} = \text{proj}_{\mathbf{v}} \mathbf{u} \)**### Detailed Explanation of Vectors:- **Vector \( \mathbf{a} = -\mathbf{u} \)**: This is the vector \( \mathbf{u} \) but with the opposite direction. - **Vector \( \mathbf{b} = 2\mathbf{v} \)**: This vector is twice the magnitude of \( \mathbf{v} \) in the same direction.- **Vector \( \mathbf{s} = \mathbf{v} + \mathbf{u} \)**: This is the resultant vector from the vector addition of \( \mathbf{v} \) and \( \mathbf{u} \).- **Vector \( \mathbf{d} = \mathbf{v} - \mathbf{u} \)**: This is the resultant vector from the vector subtraction of \( \mathbf{u} \) from \( \mathbf{v} \).- **Vector \( \mathbf{p} = \text{proj}_{\mathbf{v}} \mathbf{u} \)**: This is the projection of \( \mathbf{u} \) onto \( \mathbf{v} \), showing how much of \( \mathbf{u} \) acts in the direction of \( \mathbf{v} \).### Visualization:Please graph the above vectors \( \mathbf{a

Answered: Image /qna-images/answer/2fad8336-097d-4acd-9466-be217261d513.jpg

Answered: u V Provide graphs of the following…

u V Provide graphs of the following vectors in the space above. Label each vector appropriately. (а) а — — и (b) b= 2v (c) s = v + u (d) d = v – u (e) p = proj, u

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

**Guidelines for Drawing Coordinate Axes**

When drawing your 2- and 3-dimensional coordinate axes, follow these instructions:

1. **Labeling**: Ensure that you label the positive side of each axis clearly.
2. **Tick Marks**: Include tick marks on each axis to indicate units of measurement.
3. **Scaling**: Make sure each axis has a scale.

For 3-dimensional coordinate systems, adhere to the **right-hand rule**:

- The right-hand rule helps in determining the direction of the axes. Point your thumb, index finger, and middle finger perpendicular to each other. The thumb points in the direction of the x-axis, the index finger in the direction of the y-axis, and the middle finger in the direction of the z-axis.

**Labeling Objects**: Always label all objects you graph for clarity.

**Vector Notation**: Use appropriate vector notation whenever you are writing a vector to differentiate it from scalar quantities.

### Vectors and Their Graphical Representations

**Vectors \( \mathbf{u} \) and \( \mathbf{v} \)**

Below are graphical representations of the vectors \( \mathbf{u} \) and \( \mathbf{v} \).

![Vectors \( \mathbf{u} \) and \( \mathbf{v} \)](insert_graph_image_here)

**Instructions:**
Provide graphs of the following vectors in the space above. Label each vector appropriately.

### Vectors to be graphed:

(a) **Vector \( \mathbf{a} = -\mathbf{u} \)**

(b) **Vector \( \mathbf{b} = 2\mathbf{v} \)**

(c) **Vector \( \mathbf{s} = \mathbf{v} + \mathbf{u} \)**

(d) **Vector \( \mathbf{d} = \mathbf{v} - \mathbf{u} \)**

(e) **Vector \( \mathbf{p} = \text{proj}_{\mathbf{v}} \mathbf{u} \)**

### Detailed Explanation of Vectors:

- **Vector \( \mathbf{a} = -\mathbf{u} \)**: This is the vector \( \mathbf{u} \) but with the opposite direction.

- **Vector \( \mathbf{b} = 2\mathbf{v} \)**: This vector is twice the magnitude of \( \mathbf{v} \) in the same direction.

- **Vector \( \mathbf{s} = \mathbf{v} + \mathbf{u} \)**: This is the resultant vector from the vector addition of \( \mathbf{v} \) and \( \mathbf{u} \).

- **Vector \( \mathbf{d} = \mathbf{v} - \mathbf{u} \)**: This is the resultant vector from the vector subtraction of \( \mathbf{u} \) from \( \mathbf{v} \).

- **Vector \( \mathbf{p} = \text{proj}_{\mathbf{v}} \mathbf{u} \)**: This is the projection of \( \mathbf{u} \) onto \( \mathbf{v} \), showing how much of \( \mathbf{u} \) acts in the direction of \( \mathbf{v} \).

### Visualization:
Please graph the above vectors \( \mathbf{a

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