Given point P(-2, 6, 3) and vector B=ya_{x}+(x+z)a_{y}, express P and B in cylindrical and spherical coordinates. Evaluate A at P in the Cartesian, cylindrical and spherical systems.

Ava-May Nelson 2021-02-05 Answered
Given point P(-2, 6, 3) and vector B=yax+(x+z)ay, express P and B in cylindrical and spherical coordinates. Evaluate A at P in the Cartesian, cylindrical and spherical systems.
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

dieseisB
Answered 2021-02-06 Author has 85 answers

Step 1 The objective is to express the point P(−2,6,3) and vector B=yax+(x+z)ay in cylindrical and spherical coordinates. Step 2 To convert Cartesian coordinates (x,y,z) to cylindrical coordinates (r,θ,z) r=x2+y2
θ=tan1(yx)
z=z The point P(2,6,3) in cylindrical coordinates is, r=4+36
=40
=210 And θ=tan1(62)
=1.25 Cylindrical coordinates is (210,1.25,3) To convert Cartesian coordinates (x,y,z) to spherical coordinates (ρ,θ,ϕ) p=x2+y2+z2
θ=tan1(yx)
ϕ=tan1(x2+y2z) The point P(2,6,3) in spherical coordinates is, p=x2+y2+z2
4+36+9
=49
=7 And θ=tan1(62)
=1.25 And ϕ=tan1(4+363)
=tan1(403)
=1.3034 Spherical coordinates is (7,1.25,1.3034) Step 3 The vector B=yax+(x+z)ay in cylindrical and spherical coordinates. In the cartesian system B at P is B=6ax+ay For vector B, Bx=y
By=x+z
Bz=0 In cylindrical system Ar=ycosθ+(x+z)sinθ
Aθ=ysinθ+(x+z)cosθ

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more