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Space is referred to an orthonormal coordinate system \((O; \Vect{i}, \Vect{j}, \Vect{k})\).Consider the points \(A(10, 0, 1)\), \(B(1, 7, 1)\), and \(C(0, 0, 5)\).
    1. Show that the lines \((OA)\) and \((OB)\) are not perpendicular.
    2. Determine the measure of the angle \(\Angle{AOB}\), rounded to the nearest \(0.1^{\circ}\).
  2. Verify that \(7x + 9y - 70z = 0\) is a Cartesian equation of the plane \((OAB)\).
  3. Give a parametric representation of the line \((CA)\).
  4. Let \(D\) be the midpoint of segment \([OC]\). Determine an equation of the plane \(\mathscr{P}\) parallel to the plane \((OAB)\) and passing through \(D\).
  5. The plane \(\mathscr{P}\) intersects line \((CB)\) at \(E\) and line \((CA)\) at \(F\). Determine the coordinates of point \(F\). (It is given that \(E\) has coordinates \((\frac{1}{2}, \frac{7}{2}, 3)\)).
  6. Show that the line \((EF)\) is parallel to the line \((AB)\).

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