3-Dimensional Space

Practice Questions

Calculus 3 › 3-Dimensional Space

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$\begin{align*}&\text{A point in space is located, in Cartesian coordinates, at }(-32,52,73).\&\text{What is the position of this point in spherical coordinates?}\end{align*}$

$\begin{align*}&\text{A point in space is located, in Cartesian coordinates, at }(38,82,130).\&\text{What is the position of this point in spherical coordinates?}\end{align*}$

$\begin{align*}&\text{A point in space is located, in Cartesian coordinates, at }(100,81,-100).\&\text{What is the position of this point in spherical coordinates?}\end{align*}$

$\begin{align*}&\text{A point in space is located, in Cartesian coordinates, at }(6,-46,-105).\&\text{What is the position of this point in spherical coordinates?}\end{align*}$

$\begin{align*}&\text{A point in space is located, in spherical coordinates, at } (19,-94^{\circ},33^{\circ})\text{ of form: } (\rho,\theta,\phi)\&\text{Where }\phi\text{ is the angle between the vector, }\rho\text{, to the point and the }z\text{ axis}.\&\text{What is the position of this point in Cartesian coordinates?}\end{align*}$

Find an equation of a sphere that has the line segment joining (0,4,2) and (6,0,2) as a diameter.

$\begin{align*}&\text{A point in space is located, in Cartesian coordinates, at }(95,-77,129).\&\text{What is the position of this point in spherical coordinates?}\end{align*}$

$\begin{align*}&\text{A point in space is located, in Cartesian coordinates, at }(23,-133,-80).\&\text{What is the position of this point in spherical coordinates?}\end{align*}$

Express the three-dimensional (x,y,z) Cartesian coordinates as cylindrical coordinates (r, θ, z):

$\left ( 2,1, -2\right )$

$\begin{align*}&\text{A point in space is located, in cylindrical coordinates, at } (105,163^{\circ},-55).\&\text{What is the position of this point in Cartesian coordinates?}\end{align*}$

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