$\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

    $a(x + y + z) + b(p + q + r) + c$

  • B

    $0$

  • C

    $abc + xyz + pqr$

  • D

    None of these

Similar Questions

The value of the determinant given below $\left| {{\rm{ }}\begin{array}{*{20}{c}}1&2&3\\3&5&7\\8&{14}&{20}\end{array}} \right|$ is

The determinant $\left| {\begin{array}{*{20}{c}}{\cos \,\,(\theta \, + \,\phi )}&{ - \,\sin \,\,(\theta \, + \,\phi )}&{\cos \,2\phi }\\{\sin \,\theta }&{\cos \,\theta }&{\sin \,\phi }\\{ - \,\cos \,\theta }&{\sin \,\theta }&{\cos \,\phi }\end{array}} \right|$ is :

The system of equations  $-k x+3 y-14 z=25$  $-15 x+4 y-k z=3$  $-4 x+y+3 z=4$  is consistent for all $k$ in the set

  • [JEE MAIN 2022]

The value of $\lambda$ and $\mu$ such that the system of equations $x+y+z=6,3 x+5 y+5 z=26, x+2 y+\lambda z=\mu$ has no solution, are :

  • [JEE MAIN 2021]

Let the area of the triangle with vertices $A (1, \alpha)$, $B (\alpha, 0)$ and $C (0, \alpha)$ be $4\, sq.$ units. If the point $(\alpha,-\alpha),(-\alpha, \alpha)$ and $\left(\alpha^{2}, \beta\right)$ are collinear, then $\beta$ is equal to

  • [JEE MAIN 2022]