to be continued

If c is wrong, first determine the trajectory of point p, and then use the space vector to find the maximum value.

to be continued

Option d, according to the fact that the planes where two straight lines on different planes are parallel and the distance between parallel planes is 1/3 of the diagonal of the object, the distance between two straight lines on different planes is equal to √3/3. So d is correct.

For your reference, please take it.