Chapter 14.1, Problem 16PSB

a.

To determine

To find the locus in space of points.

Answer to Problem 16PSB

A sphere of radius $5$ centered at the point.

Explanation of Solution

Given:

The point is $5$ units from a given point.

Calculation:

The sphere will contain all points in space equidistant from a single point.

b.

To determine

To find the locus in space of points.

Answer to Problem 16PSB

An infinite cylindrical tube of radius $5$ with the central axis on the line.

Explanation of Solution

Given:

The point is $5$ units from a given line.

Calculation:

A Cylinder will contain all the points around a line that is equidistant from the line. It extends infinitely in both directions because the line also extends infinitely.