| , * 20 c a - b & b - c & c - a x - y & y - z & z - x p - q & q … - Vidyadip

MCQ

$\left| {\,\begin{array}{*{20}{c}}{a - b}&{b - c}&{c - a}\\{x - y}&{y - z}&{z - x}\\{p - q}&{q - r}&{r - p}\end{array}\,} \right| = $

A
$a(x + y + z) + b(p + q + r) + c$
✓
$0$
C
$abc + xyz + pqr$
D
None of these

✓

Answer

Correct option: B.

$0$

b
(b) $\left| {\,\begin{array}{*{20}{c}}
{a - b}&{b - c}&{c - a}\\
{x - y}&{y - z}&{z - x}\\
{p - q}&{q - r}&{r - p}
\end{array}\,} \right| = \left| {\,\begin{array}{*{20}{c}}
0&{b - c}&{c - a}\\
0&{y - z}&{z - x}\\
0&{q - r}&{r - p}
\end{array}\,} \right| = 0$

$[by {C_1} \to {C_1} + {C_2} + {C_3}]$

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