Question

Given the point A (x = 2, y = 3, z = −1) and B(r = 4, θ = 250

, Φ = 1200

), find

(a) The spherical co-ordinates of A.


(b) The Cartesian co-ordinates of B.

(c) The distance from A to B.​

Answer 1

Answer:

To convert a point from Cartesian coordinates to spherical coordinates, use equations ρ2=x2+y2+z2,tanθ=yx, and φ=arccos(z√x2+y2+z2). To convert a point from spherical coordinates to cylindrical coordinates, use equations r=ρsinφ,θ=θ, and z=ρcosφ.

Answer 2

The complete solution is in the images.

Here θ=25° and Φ=120°