(a) The correct option is: (A) 3
When the space is two dimensional, two coordinates are needed to specify the location of the rigid body, however there is no information about its orientation. Therefore one needs another account to account for the orientation of the rigid body. This makes the total number of coordinates to be 3.
Hence, the correct option is (A), while the others are ruled out.
(b) The correct option is: (B) 2
When the space is one dimensional, one coordinate is needed to specify the location of the rigid body, however, there is no information regarding the orientation of the body. Therefore one needs another coordinate to account for the orientation of the rigid body.
Therefore the total number of coordinates needed to account for both location and orientation of the rigid body is 2.
Hence (B) is the correct option, and the others are ruled out.
(c) The correct option is (A) 7
When the space is 4-dimensional, four coordinates are needed to specify the location of the object. However this will not include ant information regarding the orientation of the body. If one chooses a reference axis from the four location coordinates, three additional coordinates will be needed to account for the orientation of the rigid body with respect to that reference axis.
Therefore, the total number of coordinates needed to define both location and orientation of the rigid body is 7.
Hence (A) is the correct option, while the others are ruled out.