Under which of the following conditions does the determinant \(\begin{vmatrix} 1+a&1 & 1 \\ 1 & 1+b & 1 \\ 1& 1 & 1+c \\ \end{vmatrix}\) vanish?
1. abc = 0
2. abc + bc + ca + ab = 0
3. \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=0\)
Select the correct answer using the code given below:
1
1 and 2 only
2
2 and 3 only
3
1 and 3 only
4
1, 2 and 3