**Title: Vector Calculation Practice****Objective:**Find \(2\mathbf{u}\), \(-4\mathbf{v}\), \(\mathbf{u} + \mathbf{v}\), and \(4\mathbf{u} - 5\mathbf{v}\) for the given vectors \(\mathbf{u}\) and \(\mathbf{v}\). Simplify your answers completely.**Given:**- \(\mathbf{u} = \mathbf{i} + \mathbf{j}\)- \(\mathbf{v} = \mathbf{i} - \mathbf{j}\)**Calculations and Answers:**1. **Calculate \(2\mathbf{u}\):** \[2\mathbf{u} = 2(\mathbf{i} + \mathbf{j}) = 2\mathbf{i} + 2\mathbf{j}\] *[Incorrect]*2. **Calculate \(-4\mathbf{v}\):** \[-4\mathbf{v} = -4(\mathbf{i} - \mathbf{j}) = -4\mathbf{i} + 4\mathbf{j}\] *[Incorrect]*3. **Calculate \(\mathbf{u} + \mathbf{v}\):** \[\mathbf{u} + \mathbf{v} = (\mathbf{i} + \mathbf{j}) + (\mathbf{i} - \mathbf{j})\] \[= 2\mathbf{i} - 0\mathbf{j} = 2\mathbf{i}\] *[Correct]*4. **Calculate \(4\mathbf{u} - 5\mathbf{v}\):** \[4\mathbf{u} - 5\mathbf{v} = 4(\mathbf{i} + \mathbf{j}) - 5(\mathbf{i} - \mathbf{j})\] \[= 4\mathbf{i} + 4\mathbf{j} - 5\mathbf{i} + 5\mathbf{j}\] \[= (\mathbf{i} + 9\mathbf{j})\] *[Incorrect]***Note:** The boxes next to each calculation indicate their correctness, with an "X" marking incorrect answers and shaded area highlighting a correct answer.

Answered: Image /qna-images/answer/cd0da29f-e6c5-4750-9724-67bf01ed2fd3.jpg

Answered: Find 2u, -4v, u + v, and 4u – 5v for…

Find 2u, -4v, u + v, and 4u – 5v for the given vectors u and v. (Simplify your answers completely.) u = i+j, v = i - j 2u = 2i + 2j -4i + 4j -4v = 2i – 2j u + v = 4u - 5v = -i+ 9j

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

**Title: Vector Calculation Practice**

**Objective:**
Find \(2\mathbf{u}\), \(-4\mathbf{v}\), \(\mathbf{u} + \mathbf{v}\), and \(4\mathbf{u} - 5\mathbf{v}\) for the given vectors \(\mathbf{u}\) and \(\mathbf{v}\). Simplify your answers completely.

**Given:**
- \(\mathbf{u} = \mathbf{i} + \mathbf{j}\)
- \(\mathbf{v} = \mathbf{i} - \mathbf{j}\)

**Calculations and Answers:**

1. **Calculate \(2\mathbf{u}\):**

\[2\mathbf{u} = 2(\mathbf{i} + \mathbf{j}) = 2\mathbf{i} + 2\mathbf{j}\]

*[Incorrect]*

2. **Calculate \(-4\mathbf{v}\):**

\[-4\mathbf{v} = -4(\mathbf{i} - \mathbf{j}) = -4\mathbf{i} + 4\mathbf{j}\]

*[Incorrect]*

3. **Calculate \(\mathbf{u} + \mathbf{v}\):**

\[\mathbf{u} + \mathbf{v} = (\mathbf{i} + \mathbf{j}) + (\mathbf{i} - \mathbf{j})\]
\[= 2\mathbf{i} - 0\mathbf{j} = 2\mathbf{i}\]

*[Correct]*

4. **Calculate \(4\mathbf{u} - 5\mathbf{v}\):**

\[4\mathbf{u} - 5\mathbf{v} = 4(\mathbf{i} + \mathbf{j}) - 5(\mathbf{i} - \mathbf{j})\]
\[= 4\mathbf{i} + 4\mathbf{j} - 5\mathbf{i} + 5\mathbf{j}\]
\[= (\mathbf{i} + 9\mathbf{j})\]

*[Incorrect]*

**Note:** The boxes next to each calculation indicate their correctness, with an "X" marking incorrect answers and shaded area highlighting a correct answer.

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