本题目来源于试卷: VectorsVectors，类别为 IB数学
[问答题]
A line L has equats/2;i nv /huuwio h /w0,px7v,t(f4q/mx mwzhmfns $ \frac{x-a}{2}=\frac{y-1}{b}=-\frac{z-1}{2}$ where a, b $\in \mathbb{Z}$ .
A plane $ \Pi $ has equation 2 x+3 y-z=6 .
1. Show that L is not perpendicular to $\Pi$ .
2. Given that L lies in the plane $\Pi $, find the value of a and the value of b .
Consider the different case where the acute angle between L and $ \Pi$ is $\alpha $ where $ \alpha=\arcsin \left(\frac{3}{\sqrt{14}}\right)$.
3. 1. Show that b=1 .
2. Given that L intersects $ \Pi$ at z=-3 , find the value of a .
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