Q: Given vectors $ \mathbf{u} = \langle 3, -2 \rangle $ and $ \mathbf{v} = \langle -1, 4 \rangle $, demonstrate how vector subtraction can be understood as adding the additive inverse. Calculate $ \mathbf{u} - \mathbf{v} $ and explain each step of your solution.

To find $ \mathbf{u} - \mathbf{v} $, we take the vector $ \mathbf{u} = \langle 3, -2 \rangle $ and add the additive inverse of $ \mathbf{v} = \langle -1, 4 \rangle $. The additive inverse of $ \mathbf{v} $ is $ -\mathbf{v} = \langle 1, -4 \rangle $. Thus, $ \mathbf{u} - \mathbf{v} = \mathbf{u} + (-\mathbf{v}) = \langle 3, -2 \rangle + \langle 1, -4 \rangle = \langle 3+1, -2-4 \rangle = \langle 4, -6 \rangle $.

Question 1

Which of the following statements correctly describe New Jersey's role in the Underground Railroad and the growing resistance to slavery in the 19th century? Select all that apply.

Accepted Answer

New Jersey was a major hub for the Underground Railroad, providing routes for escaped slaves to reach freedom.; Several abolitionist groups in New Jersey actively worked to end slavery and assist escaped slaves.

Question 2

Which of the following scenarios best illustrates the importance of due process in protecting individual rights?

Accepted Answer

C

Question 3

How did New Jersey's geographic location impact the outcomes of the American Revolution?

Accepted Answer

New Jersey's central location made it a strategic crossroads for military campaigns.

Question 4

Construct a well-developed argument that prioritizes the causes and events leading to the Civil War. Be sure to include perspectives from multiple sources, such as political leaders, abolitionists, and Southern landowners. Explain how these perspectives contributed to the different priorities and tensions that ultimately resulted in the Civil War.

Accepted Answer

A comprehensive argument should include various causes and events such as the economic differences between the North and South, the impact of the abolitionist movement, and political compromises like the Missouri Compromise and the Kansas-Nebraska Act. Perspectives from political leaders might focus on states' rights and federal authority, while abolitionists would highlight the moral imperative to end slavery. Southern landowners may prioritize the preservation of their economic system based on slavery. Each perspective contributed to a growing divide, with differing priorities leading to increased tensions and ultimately, the outbreak of the Civil War.

Question 5

When considering a local budget issue, why is it important to seek the perspectives of multiple stakeholders?

Accepted Answer

B) It helps to understand different needs and priorities within the community.

Question 6

Given vectors $ \mathbf{u} = \langle 3, -2 \rangle $ and $ \mathbf{v} = \langle -1, 4 \rangle $, demonstrate how vector subtraction can be understood as adding the additive inverse. Calculate $ \mathbf{u} - \mathbf{v} $ and explain each step of your solution.

Accepted Answer

To find $ \mathbf{u} - \mathbf{v} $, we take the vector $ \mathbf{u} = \langle 3, -2 \rangle $ and add the additive inverse of $ \mathbf{v} = \langle -1, 4 \rangle $. The additive inverse of $ \mathbf{v} $ is $ -\mathbf{v} = \langle 1, -4 \rangle $. Thus, $ \mathbf{u} - \mathbf{v} = \mathbf{u} + (-\mathbf{v}) = \langle 3, -2 \rangle + \langle 1, -4 \rangle = \langle 3+1, -2-4 \rangle = \langle 4, -6 \rangle $.

Create Standards-Aligned Questions Instantly

Sample Question of the Day

Recent Questions