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\textbf{Assignment on Lines }

\begin{enumerate}
\item Find the vector and parametric equations for the line through
  the point $P=(2, 5, -1)$ and parallel to the vector $\v = \la -3, 1,
  2\ra$.
  
\item Find the vector and parametric equations for the line through
  the point $P=(5, 8, -6)$ and parallel to the vector $\v = 2\i -3\j +
  4\k$.
  
\item Find the vector and parametric equations for the line through
  the points $P=(4, 1, -8)$ and $Q = (2, 3, 5)$.
  
\item Find the angle between the lines $l_1$ and $l_2$ given
  by:\newline $l_1: \r = \la 1-2t, 3+t, 4 - 5t\ra$ and $l_2: \r= \la
  2-s, 1-2s, 3+2s\ra$.
  
\item Find the parametric equations of the line through $(3, -1, 2)$
  and parallel to the line $\r = \la2-3t, 7+t,8+5t\ra$.
  
\item Find the vector form of the line through the point $(5, 2, -3)$
  and orthogonal to the lines $\r = \la 2+t, 3-2t, 4 - 5t\ra$ and $\r
  = \la 1-t, 2t, 3+4t \ra$.
  
\item Determine whether the lines $l_1$ and $l_2$ are parallel, skew,
  or intersecting.  If they intersect, find their point of
  intersection.
  \begin{enumerate}
  \item $l_1$: $x = 4 - t$, $y = 2t$, $z = 3 + 4t$, and $l_2$: $x = 2
    + 3s$, $y = 1 - s$, $z = 4 + s$.
    
  \item $l_2$: $\r = \la 3 - 4t, 2 + t, 2t \ra$, and $\r = \la 3 + 2s,
    1-s, 8 + 3s \ra$
  \end{enumerate}

\end{enumerate}







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