\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} a) Suppose that $\bf a$ and $\bf b$
are three-dimensional vectors and that $\|{\bf a}\|=10$ and $\|{\bf
b}\|=8$.  How big could $\|{\bf a}+{\bf b}\|$ be?  How small?  Give a
geometric argument as to why your answer is correct.

\medskip

\noindent b) Suppose that in a) we know only that $8\le \|{\bf a}\|\le
12$ and $7 \le \|{\bf b}\|\le 9$.  Answer the same questions.

\medskip 

\noindent c) Suppose we know that $\|\bf a\|=10$, $\|\bf b\|=6$, and
$9<\|{\bf a}+{\bf b}\|<11$. What information is there about the angle
between $\bf a$ and $\bf b$?
  
\vfil\eject\end