The value of the determinant $\begin{vmatrix}1 & x & y+z\\1 & y & z+x\\1 & z & x+y \end{vmatrix}$ is :

0 xyz $x+y +z+1$ $3xyz$

0

The correct answer is Option (1) → 0 $Δ=\begin{vmatrix}1 & x & y+z\\1 & y & z+x\\1 & z & x+y \end{vmatrix}$ $C_3→C_3+C_2$ $Δ=\begin{vmatrix}1 & x & x+y+z\\1 & y & x+y+z\\1 & z & x+y+z\end{vmatrix}=0$ as $C_1$ and $C_3$ are proportional