AP EAMCET · Maths · Three Dimensional Geometry
If \(S\) is the set of all real values of ' \(a\) ' such that a plane passing through the points \(\left(-\mathrm{a}^2, 1,1\right),\left(1,-\mathrm{a}^2, 1\right)\), \(\left(1,1,-\mathrm{a}^2\right)\) also passes through the point \((-1,-1,1)\), then \(\mathrm{S}=\)
- 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
Since all four points are coplaner \(\begin{aligned} & \Rightarrow\left|\begin{array}{ccc} 1-a^2 & 2 & 0 \\ 2 & -a^2+1 & 0 \\ 2 & 2 & -a^2-1 \end{array}\right|=0 \Rightarrow\left(a^2+1\right)^2\left(3-a^2\right)=0 \\ & \Rightarrow a= \pm \sqrt{3} \end{aligned}\) So,…
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