The determinant | , * 20 c a&b& a - b &c& b - c 2&1&0 , | is equa… - Vidyadip

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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