Solved Examples/Numericals On Coordinate System & Transformation - 2.
Q.7 Calculate the distance between the following pair of points? a) (2, 1, 5) and (6, -1, 2) b) (3, π/2, -1) and (5, 3π/2, 5) c) (10, π/4, 3π/4) and (5, π/6, 7π/4) Ans. a) Distance between two points in Cartesian co-ordinate is given as: d 2 = (x 2 – x 1 ) 2 +(y 2 – y 1 ) 2 +(z 2 – z 1 ) 2 = (6 – 2) 2 + (-1 -1) 2 + (2 – 5) 2 = (29) 1/2 => d = 5.38 b) Distance between two points in cylindrical co-ordinate system is given as: d 2 = ρ 2 2 + ρ 1 2 - 2ρ 1 ρ 2 cos(φ 2 – φ 1 ) + (z 2 – z 1 ) 2 = 5 2 + 3 2 – 2.5.3 cos(3π/2 - π/2) + (5 +1) 2 = (100) 1/2 => d = 10. c) Distance between two points in spherical co-ordinate system is given as: d 2 = r 2 2 + r 1 2 – 2r 1 r 2 cosθ 2 cosθ 1 + 2r 1 r 2 sinθ 2 sinθ 1 cos(φ 2 – φ 1 ) = 10 2 + 5 2 – 2.5.10 cosπ/4 cosπ/6 + 2.5.10 sinπ/4 sinπ/6 cos(7π/4 - 3π/4) = (99.12) 1/2 => d = 9.96 Q.8 Find the distance between A (2, π /6, 0) and B = (1, π /2, 2) ? Ans: T...