(688,#3) a)Draw a rectangular box that has P(1,1,2) and Q(3,4,5) as opposite vertices and has its faces parallel to the coordinate planes

(688,#3) a) Draw a rectangular box that has P(1,1,2) and Q(3,4,5) as opposite vertices and has its faces parallel to the coordinate planes;
b)Find the coordinates of the other six vertices of the box;
c) Find the length of the diagonal of the box;
Solution: a)

b)

c) Distance formula in three dimensions for the distance between the points
is:

Therefore the length of the diagonal is the distance between the points P(1,1,2) and Q(3,4,5) :

by:sh