**Vectors Subtraction and Scalar Multiplication**In this instructional guide, we will analyze the graphical representation of vectors and learn about their operations, such as subtraction and scalar multiplication.**Graph Description:**In the provided graph, vectors \( \mathbf{u} \) and \( \mathbf{v} \) are illustrated in a 2-dimensional coordinate plane.- The horizontal axis represents the x-axis, while the vertical axis indicates the y-axis.- The coordinate system ranges from -10 to 10 on both axes.**Vector \( \mathbf{u} \):**- Vector \( \mathbf{u} \) starts at the origin (0, 0) and terminates at the point (-5, -5).- It is directed towards the third quadrant, pointing downwards and to the left.**Vector \( \mathbf{v} \):**- Vector \( \mathbf{v} \) starts at the origin (0, 0) and terminates at the point (7, 5).- It is directed towards the first quadrant, pointing upwards and to the right.**Question:**What is \(-3(\mathbf{u} - \mathbf{v})\)?**Operation Explanation:**To find the vector resulting from \(-3(\mathbf{u} - \mathbf{v})\), follow these steps:1. **Vector Subtraction (\(\mathbf{u} - \mathbf{v}\)):** - \(\mathbf{u} = <-5, -5>\) - \(\mathbf{v} = <7, 5>\) - \(\mathbf{u} - \mathbf{v} = <-5, -5> - <7, 5> = <-5 - 7, -5 - 5> = <-12, -10>\)2. **Scalar Multiplication (\(-3(\mathbf{u} - \mathbf{v})\)):** - Multiply the resulting vector by -3: - \(-3(\mathbf{u} - \mathbf{v}) = -3<-12, -10> = <36, 30>\)Thus, the vector \(\-3(\mathbf{u} - \mathbf{v})\) is \(<36, 30>\).**Conclusion:**Understanding these operations, vector subtraction, and scalar multiplication can help apply these concepts to various fields such as physics The image contains a list of variables denoted by letters and their corresponding numerical values. Here's the transcription suitable for an educational website:---### Variable Values- **a**: 270 - **b**: 258 - **c**: 90 - **d**: -86 These values might represent data points in a statistical analysis, coefficients in an equation, or a sequence in a numerical problem. Be sure to interpret them within the context of their application.---

Answered: Image /qna-images/answer/6d7e9d75-5c34-4774-a5e0-a4ca60d7afc5.jpg

Answered: Vectors u and v are shown in the graph.…

Math

Trigonometry

Vectors u and v are shown in the graph. -10-9-8-7-6-5-4-3-2-1 What is -3(u-v)? u 7 3 2 1 -7 -10 O 1 2 3 4 5 6 7 8

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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Question

**Vectors Subtraction and Scalar Multiplication**

In this instructional guide, we will analyze the graphical representation of vectors and learn about their operations, such as subtraction and scalar multiplication.

**Graph Description:**

In the provided graph, vectors \( \mathbf{u} \) and \( \mathbf{v} \) are illustrated in a 2-dimensional coordinate plane.

- The horizontal axis represents the x-axis, while the vertical axis indicates the y-axis.
- The coordinate system ranges from -10 to 10 on both axes.

**Vector \( \mathbf{u} \):**

- Vector \( \mathbf{u} \) starts at the origin (0, 0) and terminates at the point (-5, -5).
- It is directed towards the third quadrant, pointing downwards and to the left.

**Vector \( \mathbf{v} \):**

- Vector \( \mathbf{v} \) starts at the origin (0, 0) and terminates at the point (7, 5).
- It is directed towards the first quadrant, pointing upwards and to the right.

**Question:**

What is \(-3(\mathbf{u} - \mathbf{v})\)?

**Operation Explanation:**

To find the vector resulting from \(-3(\mathbf{u} - \mathbf{v})\), follow these steps:

1. **Vector Subtraction (\(\mathbf{u} - \mathbf{v}\)):**
- \(\mathbf{u} = <-5, -5>\)
- \(\mathbf{v} = <7, 5>\)
- \(\mathbf{u} - \mathbf{v} = <-5, -5> - <7, 5> = <-5 - 7, -5 - 5> = <-12, -10>\)

2. **Scalar Multiplication (\(-3(\mathbf{u} - \mathbf{v})\)):**
- Multiply the resulting vector by -3:
- \(-3(\mathbf{u} - \mathbf{v}) = -3<-12, -10> = <36, 30>\)

Thus, the vector \(\-3(\mathbf{u} - \mathbf{v})\) is \(<36, 30>\).

**Conclusion:**

Understanding these operations, vector subtraction, and scalar multiplication can help apply these concepts to various fields such as physics

The image contains a list of variables denoted by letters and their corresponding numerical values. Here's the transcription suitable for an educational website:

---

### Variable Values

- **a**: 270
- **b**: 258
- **c**: 90
- **d**: -86

These values might represent data points in a statistical analysis, coefficients in an equation, or a sequence in a numerical problem. Be sure to interpret them within the context of their application.

---

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