Q. 21 - Calculus

Question

What is the set of all position vectors in \(R^3\) of magnitude \(5\)? 

Step-by-Step Solution

Answer

It is the set of all the position vectors whose terminal points are on the sphere with a radius of \(5\) and a center at the origin.

Step 1. Given Information

All position vectors in \(R^3\) with magnitude \(5\).

Step 2. Find the set of position vectors

Consider the following graph

The graph shows the vector with a magnitude of \(5\).

The set of all position vectors in \(R^3\) with magnitude \(5\) is the set of all the position vectors whose terminal points are on the sphere with radius \(5\) and center at the origin.