本题目来源于试卷: VectorsVectors，类别为 IB数学
[问答题]
Consider the planes tygr(rs(um 6 *ztk cdt2y,5- pg ow-m1 $\Pi_{1}$, $\Pi_{2}$, $\Pi_{3}$ given by the following equations:
$\begin{array}{lr}
\Pi_{1}: & 2 x+y-z=-3 \\
\Pi_{2}: & x+5 y-5 z=-6 \\
\Pi_{3}: & 3 x+5 y-5 z=-7
\end{array}
$
1. Show that the three planes do not intersect.
It is given that the point $\mathrm{Q}(-1,-1,0)$ lies on both $\Pi_{1}$ and $\Pi_{2} $.
Let $\ell$ be the line of intersection of $\Pi_{1}$ and $\Pi_{2} $.
2. Find a vector expression for $ \ell$ .
3. Show that $\ell$ is parallel to plane $\Pi_{3}$ .
4. Hence or otherwise, find the distance between $\ell$ and $\Pi_{3}$ Express your answer in the form $\frac{p}{\sqrt{q}}$ , where p, q$\in \mathbb{Z}$ .
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