AP EAMCET · Maths · Determinants
If the lines \(x+2 a y+a=0, x+3 b y+b=0, x+4 c y+c=0\) are concurrent, then \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) are in
- A \(\text { Arithmetic Progression }\)
- B Geometric Progression
- C Harmonic Progression
- D Arithmetico-geometric Progression
Answer & Solution
Correct Answer
(C) Harmonic Progression
Step-by-step Solution
Detailed explanation
\( \begin{vmatrix} 1 & 2a & a \\ 1 & 3b & b \\ 1 & 4c & c \end{vmatrix} = 0 \) \( 1(3bc - 4bc) - 2a(c - b) + a(4c - 3b) = 0 \) \( -bc - 2ac + 2ab + 4ac - 3ab = 0 \) \( 2ac - ab - bc = 0 \) \( 2ac = ab + bc \) \( \frac{2}{b} = \frac{1}{c} + \frac{1}{a} \) \(a, b, c\) are in…
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