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 :

Question

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Answer: D. \left\{ {\sqrt 3 , - \sqrt 3 } ight\} 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} } ight| = 0 (\lambda 2 + 1)2 (3 - \lambda 2) = 0 \lambda = \pm \sqrt 3

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 :

Answer

Explanation

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