A) \[\left\{ \sqrt{3} \right\}\]
B) \[\left\{ \sqrt{3},-\sqrt{3} \right\}\]
C) \[\left\{ 1,-1 \right\}\]
D) \[\left\{ 3,-3 \right\}\]
Correct Answer: B
Solution :
All four points are coplanar so |
\[\left| \begin{matrix} 1-{{\lambda }^{2}} & 2 & 0 \\ 2 & -{{\lambda }^{2}}+1 & 0 \\ 2 & 2 & -{{\lambda }^{2}}-1 \\ \end{matrix} \right|=0\] |
\[{{({{\lambda }^{2}}+1)}^{2}}(3-{{\lambda }^{2}})=0\] |
\[\lambda =\pm \sqrt{3}.\] |
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