<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\documentclass[a4paper,12pt]{article}
\newcommand{\ds}{\displaystyle}
\begin{document}
\parindent=0pt

{\bf Question}

Find the relative velocity of particle $A$ to particle $B$ when
the velocities of each particle is given by:
\begin{description}
\item[(i)]
${\bf v}_{A} = {\bf i} + {\bf j}$ and ${\bf v}_B = 5 {\bf i} +
2{\bf j}$

\item[(ii)]
$\ds {\bf v}_{A} = {\bf i} - {\bf j} +{\bf k} $ and ${\bf v}_B = -
{\bf i} + 6{\bf j} - 7{\bf k}$

\end{description}

\vspace{.25in}

{\bf Answer}
\begin{description}
\item[(i)]
$\ds {\bf v}_{AB} = {\bf v}_A - {\bf v}_B = {\bf i} + {\bf j} - (5
{\bf i} + 2{\bf j}) = -4{\bf i} - {\bf j}$


\item[(ii)]
$\ds {\bf v}_{AB} = {\bf i} - {\bf j} +{\bf k}- (- {\bf i} + 6{\bf
j} - 7{\bf k}) = 2{\bf i} - 7{\bf j} + 8{\bf k}$

\end{description}



\end{document}
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