If \( \mathrm{a}+\mathrm{x}=\mathrm{b}+\mathrm{y}=\mathrm{c}+\mathrm{z}+1 \), where \( \mathrm{a}, \mathrm{b}, \mathrm{c…

If \( \mathrm{a}+\mathrm{x}=\mathrm{b}+\mathrm{y}=\mathrm{c}+\mathrm{z}+1 \), where \( \mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{x}, \mathrm{y}, \mathrm{z} \) are non-zero distinct real numbers, then \( \left|\begin{array}{lll}x & a+y & x+a \\ y & b+y & y+b \\ z & c+y & z+c\end{array}\right| \) is equal to

[JEE Main 2020, 5 Sep (Shift 2)]