JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let for any three distinct consecutive terms \(a, b, c\) of an \(A.P,\) the lines \(a x+b y+c=0\) be concurrent at the point \(\mathrm{P}\) and \(\mathrm{Q}(\alpha, \beta)\) be a point such that the system of equations \( x+y+z=6, \) \( 2 x+5 y+\alpha z=\beta\) and \(x+2 y+3 z=4\), has infinitely many solutions. Then \((P Q)^2\) is equal to ...........
- A \(123\)
- B \(113\)
- C \(421\)
- D \(131\)
Answer & Solution
Correct Answer
(B) \(113\)
Step-by-step Solution
Detailed explanation
\(\because \mathrm{a}, \mathrm{b}, \mathrm{c}\) and in \(A.P\) \(\Rightarrow 2 \mathrm{~b}=\mathrm{a}+\mathrm{c} \Rightarrow \mathrm{a}-2 \mathrm{~b}+\mathrm{c}=0\) \(\therefore \mathrm{ax}+\mathrm{by}+\mathrm{c}\) passes through fixed point \((1,-2)\)…
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