Answer
$a\sqrt{3}$
Work Step by Step
Note the right triangle formed in solving part (d) -see image below.
The leg of the triangle in the xy plane is the diagonal of a square with side a ... and its length is $a\sqrt{2}$.
The other leg is a.
The hypotenuse is the body diagonal with lenth $v$. Using the Pythagorean theorem:
$v^{2}=a^{2}+(a\sqrt{2})^{2}$
$v^{2}=3a^{2}$
$v=a\sqrt{3}$
Due to symmetry, all body diagonals have this length.
