If $a,b,c$ are non zero real numbers,then $\begin{vmatrix}bc&ca&ab\\ca&ab&bc\\ab&bc&ca\end{vmatrix}$ vanishes when

Question

$\begin{array}{1 1}(A)\;\large\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\normalsize =0\\(B)\;\large\frac{1}{a}-\frac{1}{b}-\frac{1}{c}\normalsize =0\\(C)\;\large\frac{1}{b}+\frac{1}{c}+\frac{1}{a}\normalsize =0\\(D)\;\large\frac{1}{b}-\frac{1}{c}-\frac{1}{a}\normalsize =0\end{array}$