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

Question

$(a)\;0\qquad(b)\;x+y+z\qquad(c)\;1+x+y+z\qquad(d)\;(x-y)(y-z)(z-x)$