本题目来源于试卷: VectorsVectors，类别为 IB数学
[问答题]
The plane $\Pi$ has equation 2 x-y+z=15 .
The line L is perpendicular to the plane $\Pi $and has a vector equation
$\mathbf{r}=\left(\begin{array}{c}
1 \\
-p \\
3
\end{array}\right)+\lambda\left(\begin{array}{c}
-4 \\
2 \\
p
\end{array}\right), \quad \lambda \in \mathbb{R}$ .
1. Determine the value of p .
2. Find the coordinates of the point where L meets the plane $\Pi$ .
3. The point P(3,-1,2) does not lie on the plane $\Pi$ . Find:
1. $\overrightarrow{\mathrm{PA}}$ if A is a general point on L ;
2. $\lambda such that \overrightarrow{\mathrm{PA}} $ is perpendicular to L ;
3. the coordinates of the foot of the perpendicular from P to L ;
4. the shortest distance from P to L .
4. Given two planes 2 x-y+z=15 and x+3 y-2 z=8 , find the equation of a third plane which is perpendicular to both of these planes and which cuts the x -axis at -5 .
参考答案: 
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