(688,#1) a) Draw a rectangular box that has P(0,0,0) and Q(2,3,5) 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(0,0,0) and Q(2,3,5) :


by:sh