Find the Jacobian of the transformation $x = \rho \sin \phi \cos \theta$ , $y = \rho \sin \phi \sin \theta$ , $z = \rho \cos \phi$ .
A)$\theta$
B) $\beta ^ { 2 } \sin \phi$
C) $\rho \sin \phi$
D) $\rho ^ { 2 } \cos \phi$
E)2$\theta$
F) $\rho ^ { 2 } \sin \theta$
G) $\rho \sin \theta$
H) $\rho \cos \phi$

Question

Find the Jacobian of the transformation $x = \rho \sin \phi \cos \theta$ , $y = \rho \sin \phi \sin \theta$ , $z = \rho \cos \phi$ .
A)$\theta$
B) $\beta ^ { 2 } \sin \phi$ 
C) $\rho \sin \phi$
D) $\rho ^ { 2 } \cos \phi$ 
E)2$\theta$
F) $\rho ^ { 2 } \sin \theta$  
G) $\rho \sin \theta$ 
H) $\rho \cos \phi$

Quizplus · Accepted Answer

The Answer is B

Find the Jacobian of the Transformation x=ρsin⁡ϕcos⁡θx = \rho \sin \phi \cos \thetax=ρsinϕcosθ

Find the Jacobian of the Transformation $x = \rho \sin \phi \cos \theta$