\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(A(1,\ 2)\), \(B(5,\ 4)\), \(C(-1,\ -1)\), and \(D(5,\ 3)\).
  1. Calculate the vector \(\Vect{AB}\).
    \(\Vect{AB} = \begin{pmatrix} \input{124614}{}{3em}{2em}{}{} \\ \input{224614}{}{3em}{2em}{}{} \end{pmatrix}\)
  2. Calculate the vector \(\Vect{CD}\).
    \(\Vect{CD} = \begin{pmatrix} \input{324614}{}{3em}{2em}{}{} \\ \input{424614}{}{3em}{2em}{}{} \end{pmatrix}\)
  3. Calculate the determinant \(\det(\Vect{AB},\,\Vect{CD})\).
    \(\det(\Vect{AB},\,\Vect{CD}) = \)
  4. Are the lines \(\Line{AB}\) and \(\Line{CD}\) parallel?