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Chapter 6: Problem 99

Describe one similarity between the zero vector and the number 0.

Short Answer

Expert verified
One similarity between the zero vector and the number zero is that both of them act as 'additive identities' in their respective domains - in numbers and vectors respectively. Adding zero to any number, or the zero vector to any vector, leaves that number or vector unchanged.

Step by step solution

01

Understanding the nature of the zero vector

A zero vector, also known as null vector, is a vector which has zero magnitude and arbitrary direction. It's represented as \( \vec{0} \) or simply 0.
02

Understanding the nature of the number zero

The number zero is an integer which signifies 'nothing'. In mathematics, it is a highly essential number with distinctive properties.
03

Identifying the similarity

Both the zero vector and the number zero play a pivotal role in their respective mathematical contexts because of their 'neutral' properties. In the realm of numbers, '0' is the additive identity, meaning that any number added to zero gives the original number itself. Similarly, when a vector is added to the zero vector, the original vector remains unchanged. This is because the zero vector does not change the direction or magnitude of a given vector when added.

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Most popular questions from this chapter

Find the angle, in degrees, between \(\mathbf{v}\) and \(\mathbf{w}.\) $$\mathbf{v}=3 \cos \frac{5 \pi}{3} \mathbf{i}+3 \sin \frac{5 \pi}{3} \mathbf{j}, \quad \mathbf{w}=2 \cos \pi \mathbf{i}+2 \sin \pi \mathbf{j}$$

Will help you prepare for the material covered in the next section. Refer to Section 2.1 if you need to review the basics of complex numbers. In each exercise, perform the indicated operation and write the result in the standard form \(a+b i\). $$(-1+i \sqrt{3})(-1+i \sqrt{3})(-1+i \sqrt{3})$$

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