Answered: Find the Cartesian coordinates (x,y,z)…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Find the Cartesian coordinates (x,y,z) of a point in space such that its spherical coordinates (ρ,θ,φ) satisfies ρ=θ=φ. Plot this point. The answer is not unique.

Expert Solution

Step 1

Let us consider the point P whose spherical co-ordinates is $(ρ, θ, φ)$ and satisfies the equation

$ρ = θ = φ$

Let us consider $ρ = θ = φ = 0$

If the Cartesian co-ordinate of the point P is $(x, y, z)$ , then

$\begin{array}{rcl} x & = & ρ \sin θ \cos φ \\ = & 0 \\ y & = & ρ \sin θ \sin φ \\ = & 0 \\ z & = & ρ \cos φ \\ = & 0 \end{array}$

Hence, one point is the origin $(0, 0, 0)$

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