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Suppose that the point \(\left(\rho,\theta,\phi \right)=\left( 12, \frac{2 \pi}{3}, \frac{3 \pi}{4} \right)\) in spherical coordinates can be expressed as \((x, y, z)\) in rectangular coordinates. Find \((x+z)\).

 Dec 4, 2018
 #1
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I'm digging deep here, Rekt...!!!....LOL!!!!

 

First....let's convert these to cylindrical coordinates  (r, θ, z)

r = p sin Φ   =   12 sin 3pi/4  =  6√2

θ = θ = 2pi/3

z = p cos Φ =  12 cos 3pi/ 4 =    -6√2

 

Then....convert these to rectangular (Cartesian) coordinates (x, y, z)

x = r cos  θ =  6√2 * cos 2pi/ 3 =  6√2 (-1/2) = -3√2

y = r sin θ =   6√2 * sin 2pi/ 3 =  6√2 * √3/2 =  3√6

z =   -6√2

 

So   (x, y , z)  =   ( -3√2 ,  3√6,  -6√2 )

 

So.... x + z =  -9√2

 

 

cool cool cool

 Dec 4, 2018
edited by CPhill  Dec 4, 2018

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