### Vectors and Their Addition: Head to Tail Method#### Given Vectors:$ \vec{a} = \langle 3, -1 \rangle $ and $ \vec{b} = \langle -1, -4 \rangle $.#### Task:Represent $ \vec{a} + \vec{b} $ by using the head to tail method.#### Instructions:1. **Draw the Vectors**: - Use the Vector tool to draw the vectors. - Complete the head to tail method.2. **Specific Details**: - Draw $ \vec{a} $ first. - Then, from the terminal point of $ \vec{a} $, draw $ \vec{b} $. - Do not draw any unnecessary vectors.#### Using the Vector Tool:- **Select the Vector Tool**: Use the "Vector" option from the toolbar.- **Drawing a Vector**: Click on the initial point, then click on the terminal point to draw the vector.- **Editing Options**: You have options to move vectors, undo actions, redo actions, and reset the grid.#### Graph Explanation:- **Axes**: The graph displayed is a coordinate plane with x and y axes ranging from -10 to 10.- **Grid**: The grid is composed of small squares with one square unit each, making it easy to plot points and draw vectors accurately.- **Toolbar**: There is a toolbar on the graph with options: - **Move**: Allows you to move vectors. - **Vector**: The tool to draw vectors. - **Undo**: Reverts the last action. - **Redo**: Redoes the last undone action. - **Reset**: Clears the graph and resets it to its original state.By following these instructions, you can visually represent the addition of the two vectors $ \vec{a} $ and $ \vec{b} $ accurately on the coordinate plane using the head to tail method.

Answered: Image /qna-images/answer/6ddd4da1-62c4-4bf4-8893-31f4960cbd58.jpg

d= (4, - 1) and 6= (-1, -4). Represent a+ bby using the head to tail method. Use the Vector tool to draw the vectors, complete the head to tail method, and draw a- Do not draw any unnecessary vectors. To use the Vector tool, select the initial point and then the terminal point. + Move Vector * Undo + Redo x Reset

d= (4, - 1) and 6= (-1, -4). Represent a+ bby using the head to tail method. Use the Vector tool to draw the vectors, complete the head to tail method, and draw a- Do not draw any unnecessary vectors. To use the Vector tool, select the initial point and then the terminal point. + Move Vector * Undo + Redo x Reset

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

### Vectors and Their Addition: Head to Tail Method

#### Given Vectors:
$ \vec{a} = \langle 3, -1 \rangle $ and $ \vec{b} = \langle -1, -4 \rangle $.

#### Task:
Represent $ \vec{a} + \vec{b} $ by using the head to tail method.

#### Instructions:
1. **Draw the Vectors**:
- Use the Vector tool to draw the vectors.
- Complete the head to tail method.
2. **Specific Details**:
- Draw $ \vec{a} $ first.
- Then, from the terminal point of $ \vec{a} $, draw $ \vec{b} $.
- Do not draw any unnecessary vectors.

#### Using the Vector Tool:
- **Select the Vector Tool**: Use the "Vector" option from the toolbar.
- **Drawing a Vector**: Click on the initial point, then click on the terminal point to draw the vector.
- **Editing Options**: You have options to move vectors, undo actions, redo actions, and reset the grid.

#### Graph Explanation:
- **Axes**: The graph displayed is a coordinate plane with x and y axes ranging from -10 to 10.
- **Grid**: The grid is composed of small squares with one square unit each, making it easy to plot points and draw vectors accurately.
- **Toolbar**: There is a toolbar on the graph with options:
- **Move**: Allows you to move vectors.
- **Vector**: The tool to draw vectors.
- **Undo**: Reverts the last action.
- **Redo**: Redoes the last undone action.
- **Reset**: Clears the graph and resets it to its original state.

By following these instructions, you can visually represent the addition of the two vectors $ \vec{a} $ and $ \vec{b} $ accurately on the coordinate plane using the head to tail method.

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