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Chapter 11: Problem 1

Interpret the following statement: Points have a location, but no size or direction; nonzero vectors have a size and direction, but no location.

Short Answer

Expert verified
Answer: The main differences between points and nonzero vectors are that points have a location (coordinates) but no size or direction, while nonzero vectors have size (magnitude) and direction, but no fixed location. They can be shifted anywhere in space and still maintain their magnitude and direction.

Step by step solution

01

Understanding Points

A point is a basic element of geometry that represents a location in space. Points are represented by coordinates (e.g., x and y coordinates in two-dimensional space). These coordinates give the position of a point, but it does not have any size or direction.
02

Understanding Nonzero Vectors

A nonzero vector is a mathematical entity that represents direction and magnitude. It can be represented as an arrow with a starting point and an endpoint. Nonzero vectors have size (also called magnitude) and direction, but they do not have a fixed location.
03

Comparing Points and Nonzero Vectors

To summarize the differences between points and nonzero vectors: 1. Points have a location (coordinates), but no size or direction. 2. Nonzero vectors have size (magnitude) and direction, but no fixed location. They can be shifted anywhere in space and still maintain their magnitude and direction.

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