Chapter 10.2, Problem 73E

To determine

To describe: the set of all points $\left(x,y,z\right)$ such that $\Vert v\Vert =4$

Answer to Problem 73E

This represents represent sphere with $4$ and centre at $\left(x_1,y_1,z_1\right)$

Explanation of Solution

Given information: The initial and terminal points of $v$ are $\left(x_1,y_1,z_1\right)$ and $\left(x,y,z\right)$ respectively

Calculation:

The component form of $v$ is $\left(x-x_1,y-y_1,z-z_1\right)$ and the magnitude is $\sqrt{{\left(x-x_1\right)}^2+{\left(y-y_1\right)}^2+{\left(z-z_1\right)}^2}$

From the problem $\Vert v\Vert =4$

This means that ${\left(x-x_1\right)}^2+{\left(y-y_1\right)}^2+{\left(z-z_1\right)}^2=16$

That represent sphere with $4$ and centre at $\left(x_1,y_1,z_1\right)$