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just write the formulas of the exercises 

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For exercise (5):
1. The line \( g \) passes through the point \( D \) and is perpendicular to the plane \( W_t \).
2. The line \( g \) intersects the \( x \)-\( y \) plane at the point \( Q_t \) for \( t > 0 \).
3. The coordinates of the point \( Q_t \) are:
   \[
   Q_t \left( 6 - \frac{25}{t}, \frac{75}{4t}, 0 \right)
   \]

For exercise (6):
(I)
\[
P(6 - 6 \cdot r \mid 8 \cdot r \mid 0), \text{ with } 0 \leq r \leq 1
\]

(II)
\[
\left\{
\begin{aligned}
\frac{6 - 25}{t} &= 6 - 6 \cdot r \\
\frac{75}{4 \cdot t} &= 8 \cdot r
\end{aligned}
\right.
\]

(III)
The system (II) has no solution.

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Here are 5 follow-up questions based on the content:
1. How do we derive the coordinates of the point \( Q_t \) in the first equation?
2. What is the geometric meaning of the line \( g \) being perpendicular to the plane \( W_t \)?
3. How does the system of equations in (II) relate to the coordinates given in (I)?
4. What does it mean for a system of equations to have no solution geometrically?
5. Can you think of a situation where the system would have a solution, and how would that affect the geometry?

**Tip:** In systems of equations, having no solution often suggests parallel lines or planes that never intersect.

Determine the coordinates of the point where the line intersects the x-y plane and analyze a system of equations geometrically.

Solve the problem of determining the point where a line intersects the x-y plane and analyze a system of equations without a solution geometrically. The solution involves linear algebra and analytic geometry, suitable for students in Grades 11-12.

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