Solved Examples/Numericals On Coordinate System & Transformation - 1.
Q.1 Express the following points in Cartesian co-ordinate system. a) P1 (2, 30 o , 5) b) P2 (4, 30 o , 60 o ) Ans. a) P 1 (ρ, φ, z) → P 1 (x, y, z) x = ρ cosφ = 1cos 60 o = 0.5 y = ρ sinφ = 1sin 60 o = 0.87 z = z = 2 Therefore P 1 = (0.5, 0.87, 2) b) P 2 (r, θ, φ) → P 2 (x, y, z) x = r sinθ cosφ = 4sin 30 o cos 60 o = 1 y = r cosθ cosφ = 4cos 30 o cos 60 o = 1.73 z = r cosθ = 4cos 60 o = 3.46 Therefore P 2 = (1, 1.73, 3.46) Q.2. Express the point P (1, -4, -3) in cylindrical and spherical co-ordinates? Ans. P 1 (x, y, z) → P 1 (ρ, φ, z) P 2 (x, y, z) → P 2 (r, θ,φ) Q. 3 a) If V = XZ – XY +YZ, express V in Cylindrical co-ordinate system. b) If U = X 2 + 2Y 2 +3z 2 , express U in Spherical co- ordinates System . Ans. a) Since the equation given is a scalar equation, hence we just need to substitute the values of x, y and z in terms of ρ, φ and z. We know x = ρ cosφ and y = ρ sinφ V= xz – xy – yz = (ρ cosφ...