JEE Mains · Maths · STD 12 - 11. three dimension geometry
Let \(S\) be the set of all real values of \(\lambda \) such that a plane passing through the points \(( - {\lambda ^2},1,1),(1, - {\lambda ^2},1)\) and \((1,1, - {\lambda ^2})\) also passes through the point \((-1, -1, 1).\) Then \(S\) is equal to
- A \(\{ \sqrt 3 \} \)
- B \(\{ \sqrt 3 ,-\sqrt 3 \} \)
- C \(\{ 1, - 1\} \)
- D \(\{ 3, - 3\} \)
Answer & Solution
Correct Answer
(B) \(\{ \sqrt 3 ,-\sqrt 3 \} \)
Step-by-step Solution
Detailed explanation
All four points are coplanar so \(\left| {\begin{array}{*{20}{c}} {1 - {\lambda ^2}}&2&0\\ 2&{ - {\lambda ^2} + 1}&0\\ 2&2&{ - {\lambda ^2} - 1} \end{array}} \right| = 0\) \(\left(\lambda^{2}+1\right)^{2}\left(3-\lambda^{2}\right)=0\) \(\lambda=\pm \sqrt{3}\)
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