AP EAMCET · Maths · Determinants
If the point \(P(\alpha, \beta, \gamma)\) lies on the plane \(2 x+y+z=1\) and \([\alpha \beta \gamma]\left[\begin{array}{lll}1 & 9 & 1 \\ 8 & 2 & 1 \\ 7 & 3 & 1\end{array}\right]=\left[\begin{array}{lll}0 & 0 & 0\end{array}\right]\), then \(\alpha^2+\beta^2+\gamma^2=\)
- A 34
- B 43
- C 68
- D 86
Answer & Solution
Correct Answer
(D) 86
Step-by-step Solution
Detailed explanation
Point \(P(\alpha, \beta, \gamma)\) lies on plane \(2 x+y+z=1 \ldots\) Form Eqs. (i) and (iv), we get \[ 2 \alpha+\beta+\gamma=1 \quad \Rightarrow \alpha+\beta+\gamma=0 \quad \Rightarrow \alpha=1 \] put in Eqs. (ii) and (iii), we get \[ 1+8 \beta+7 \gamma=0 \] and…
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