## Vector Operations**Problem Statement**Given vectors **a** = \<1, -3\> and **b** = \<-2, 0\>, find the expression **4a - 2b**. Write your answer in component form.**Solution Process**To solve for **4a - 2b**, follow these steps:1. **Multiply Each Vector by the Given Scalar:** - **4a**: Multiply each component of vector **a** by 4. - \(4a = 4 \times \<1, -3\> = \<4 \times 1, 4 \times -3\> = \<4, -12\>\) - **2b**: Multiply each component of vector **b** by 2. - \(2b = 2 \times \<-2, 0\> = \<2 \times -2, 2 \times 0\> = \<-4, 0\>\)2. **Subtract the Results of the Scalar Multiplications:** - \(4a - 2b = \<4, -12\> - \<-4, 0\> = \<4 - (-4), -12 - 0\>\) - Simplifying gives: \( = \<4 + 4, -12\>\) - Final result: \( = \<8, -12\>\)Therefore, the component form of **4a - 2b** is **\<8, -12\>**.

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Answered: Given vectors a = (1, -3) and b = (-2,…

Math

Trigonometry

Given vectors a = (1, -3) and b = (-2, 0), find 4a - 2b. | Write your answer in component form. 4а - 2b %3D

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

## Vector Operations

**Problem Statement**

Given vectors **a** = \<1, -3\> and **b** = \<-2, 0\>, find the expression **4a - 2b**.

Write your answer in component form.

**Solution Process**

To solve for **4a - 2b**, follow these steps:

1. **Multiply Each Vector by the Given Scalar:**
- **4a**: Multiply each component of vector **a** by 4.
- \(4a = 4 \times \<1, -3\> = \<4 \times 1, 4 \times -3\> = \<4, -12\>\)

- **2b**: Multiply each component of vector **b** by 2.
- \(2b = 2 \times \<-2, 0\> = \<2 \times -2, 2 \times 0\> = \<-4, 0\>\)

2. **Subtract the Results of the Scalar Multiplications:**
- \(4a - 2b = \<4, -12\> - \<-4, 0\> = \<4 - (-4), -12 - 0\>\)
- Simplifying gives: \( = \<4 + 4, -12\>\)
- Final result: \( = \<8, -12\>\)

Therefore, the component form of **4a - 2b** is **\<8, -12\>**.

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