Q. $\left| \begin{matrix} a - b & b - c & c - a \\ x - y & y - \mathcal{z} & \mathcal{z -}x \\ p - q & p - r & r - p \end{matrix} \right|$ is equal to
A) $a\left( x + y + \mathcal{z} \right) + b(p + q + r) + c$
B) 0
C) $abc + xy\mathcal{z} + ppr$
D) None of the above
Explanation
(b)
$\left| \begin{matrix}
a - b & b - c & c - a \\
x - y & y - \mathcal{z} & \mathcal{z -}x \\
p - q & p - r & r - p
\end{matrix} \right| = \left| \begin{matrix}
0 & b - c & c - a \\
0 & y - \mathcal{z} & \mathcal{z -}x \\
0 & q - r & r - p
\end{matrix} \right| = 0$ ${(C}_{1} \rightarrow C_{1} + C_{2} + C_{3})$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.