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3 and 4 . determinant and metrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths3 and 4 . determinant and metrices1 Mark
MCQ
The determinant $\left| {\,\begin{array}{*{20}{c}}a&b&{a - b}\\b&c&{b - c}\\2&1&0\end{array}\,} \right|$ is equal to zero if $a,b,c$ are in
  • ✓
    $G. P.$
  • B
    $A. P.$
  • C
    $H. P.$
  • D
    None of these
✓

Answer

Correct option: A.
$G. P.$
a
(a) On expanding, $ - a(b - c) + 2b(b - c) + (a - b)(b - 2c) = 0$

==> $ - ab + ac + 2{b^2} - 2bc + ab - 2ac - {b^2} + 2bc = 0$

==> ${b^2} - ac = 0$

==> ${b^2} = ac$.

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