Answer to Question #294874 in Electrical Engineering for JAY

Question #294874

Transform the vector A = 3i – 2j – 4k at P(2,3,3) to cylindrical coordinates.

ans.-3.6j – 4k


1
Expert's answer
2022-02-08T08:50:01-0500

Given:

A=3i^2j^4k^{\bf A} = 3\hat i – 2\hat j – 4\hat k


The cylindrical coordinates are related to the cartesian ones by formulas

ρ=x2+y2ϕ=tan1yxz=z\rho=\sqrt{x^2+y^2}\\ \phi=\tan^{-1}\frac{y}{x}\\ z=z

In our case

ρ=32+(2)2=13ϕ=tan123=34z=4\rho=\sqrt{3^2+(-2)^2}=\sqrt{13}\\ \phi=\tan^{-1}\frac{-2}{3}=-34^\circ\\ z=-4

Finally

A=(13,34,4){\bf A}=(\sqrt{13},-34^\circ,-4)


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