In Fig. 3-30, a cube of edge

length a sits with one corner at the origin of an xyz coordinate system.A body diagonal is a line that ex- 1

tends from one corner to another through the center. In unit-vector

notation, what is the body diagonal that extends from the corner

at (a) coordinates (0, 0, 0), (b) coordinates (a, 0, 0), (c)

coordinates (0, a, 0), and (d) coordinates (a, a, 0)? (e) Determine

the angles that the body diagonals make with the adjacent edges.

(f) Determine the length of the body diagonals in terms of a.