Write the equation 5x + 4y + 7z = 1 in spherical coordinates

Question:

Write the equation {eq}5x + 4y + 7z = 1 {/eq} in spherical coordinates.

Convert to Spherical Coordinates:

The spherical coordinate is {eq}\; (\rho, \; \theta, \; \phi ) {/eq} and the rectangular coordinate is {eq}(x \ , \ y \ ,\ z). {/eq}

where {eq}\ \rho = \sqrt{(x)^2+(y)^2+(z)^2} \ {/eq} and {eq}\ x=\rho \sin \phi \cos \theta \ , \ y = \rho \sin \phi \sin \theta \ , \ z= \rho \cos \phi . {/eq}

To solve this problem, we need to plug in the variables {eq}x,y,z {/eq} in spherical coordinate and simplify the equation to get the desired solution.

Answer and Explanation:

We are given:

{eq}5x + 4y + 7z = 1. \\ {/eq}

Plug in {eq}\ x=\rho \sin \phi \cos \theta \ , \ y = \rho \sin \phi \sin \theta \ , \ z= \rho \cos...

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Chapter 10 / Lesson 13
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