Answer to Question #294874 in Electrical Engineering for JAY

Question

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

ans.-3.6j – 4k

Answer 1

Given:

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

The cylindrical coordinates are related to the cartesian ones by formulas

$$\rho=\sqrt{x^2+y^2}\\ \phi=\tan^{-1}\frac{y}{x}\\ z=z$$

In our case

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

Finally

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