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{\bf Question}

Given ${\bf a} = (2,1,0), \ {\bf b} =(1,2,3), \ {\bf c} =
(0,1,-2)$ find (a) ${\bf a} + {\bf b}$;\ (b) ${\bf b} - 2{\bf
a}$;\  (c) ${\bf \hat c}$;\ (d) $|{\bf b}|$

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{\bf Answer}

$${\bf a} = (2,1,0), \ {\bf b} =(1,2,3), \ {\bf c} = (0,1,-2)$$
\begin{description}
\item[(a)]
${\bf a} + {\bf b} =(2+1, 1+2, 0+3) = (3,3,3)$
\item[(b)]
${\bf b} - 2{\bf a} = (1,2,3) + (-2)(2,1,0) = (1,2,3) - (4,2,0) =
(-3,0,3)$
\item[(c)]
$\displaystyle{\bf \hat c} = \frac{{\bf c}}{|{\bf c}|} =
\frac{(0,1,-2)}{\sqrt{0^2 + 1^2 + (-2)^2}} = \left(0,
\frac{1}{\sqrt5}, \frac{-2}{\sqrt5}\right)$
\item[(d)]
$|{\bf b}| = \sqrt{2^2 + 1^2 + 3^2} = \sqrt{14}$
\end{description}


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