\begin{problem*}{3.63}
A rectangular parallelpiped has dimensions $a$, $b$, and $c$ as shown
in Figure 3.63.  \Part{a} Obtain a vector expression for the face
diagonal vector $\vect{R}_1$.  \Part{b} What is the magnitude of this
vector?  \Part{c} Notice that $\vect{R}_1$, $c\khat$, and $\vect{R}_2$
make a right triangle.  Obtain a vector expression for the body
diagonal vector $\vect{R}_2$.
\begin{center}
\begin{asy}
import graph3;
import Mechanics;

real u = 1cm;

real a = 1u;
real b = 1u;
real c = 1u;

xaxis3(Label("$x$"), 0, 1.5a);
yaxis3(Label("$y$"), 0, 1.5b);
zaxis3(Label("$z$"), 0, 1.5c);

draw(xscale3(a)*yscale3(b)*zscale3(c)*unitcube);
//Vector A = Vector((0,0,0), 
\end{asy}
\end{center}
\end{problem*}

\begin{solution}
\end{solution}
