Answer
$54.7^{o}$
Work Step by Step
Note the right triangle formed in solving part (d) -see image below.
The angle made by the vector and (in this case) the z axis can be found by the tangent ratio.
The leg of the triangle in the xy plane is the diagonal of a square with side a ... and its length is $a\sqrt2$.
The other leg is a.
$\displaystyle \tan\theta=\frac{\text{opposite leg}}{\text{adjacent leg}}=\frac{a\sqrt{2}}{a}=\sqrt{2}.$
$\theta=\tan^{-1}1.41=54.7^{o}$
Because of symmetry, we can say that this is the wanted angle for any body diagonal.
