Question

please solve this questtions with part (a) and (b)
Plot the point whose cylindrical coordinates are given. Then find the rectangular coordinates of the point. (a) 6, ਤੂੰ -4) O ਵਣ . 0 (x, y, 2) = (C

Answer 1

Consider point A with cylindrical co-ordinate giren As crio, 2) 5 (6, 5 -4) We know are polar coordinates of point's projection in xy plane Diagramatically, A = (0,0,2) is represented as 12 ФА १ Diagramatically A=cro,2)=(61. T 3 -4) represented as Att > ty 1/3 to tak - Here point les below y plane because z=-4

Converting these coordinate to rectangular coordinates by using Ercoso y = rsino srcoso 6 COJC) x - 3 2=3 ya rsino - 6 sin G) 6x 53 33 glya33 Z=-4 A= (6. -4)=(3,333,-4) Consider point B with Cylindrical representado Coordinates as BE Cr. O, z) = (4,11,2) In two dimensions (1,0)= (4.a) KY - 11/2 Cho -Y - In three dimensions : point lies can in yeplane 8 95 I point lies protot he doaco above or below -y axis Diagramatically of B 26 _T) a y Z arcoso Here point les above xy plane because za2 Using g x= 4 cos(-1)20 7x=0 y = rsino y 7 4 sin c")=-4 » YS-4 z = 2 B- (4, -ņ, 2) - (0,-4, 2)