A plane $\pi$ passes through the point (1,1,1) and is parallel to the vectors $\overrightarrow{a}=(-1,1,0)$ and $\overrightarrow{b}=(1,0,-1)\&\pi$ meets the axis in A, B and C forming the tetrahedron OABC where O is origin such that V be the volume of the tetrahedron OABC in cubic units then 2V is equal to

Equation of the plane  is A(x-1) + B(y -1)+C(z- 1) = 0 where A+ 0. B-1.C =0 and   $-\text{A}+\text{B}+\text{O}.\text{C}=0$$\Rightarrow A=B=C$
 and the equation of $\pi$  is  $x+y+z=3$. which meets the co-ordinates axes at $A(3,0,0),B(0,3,0)$  and  $C(0,0,3)$. 
So volume of the tethadron.  $OABC=\frac{1}{6}\left|\begin{array}{cccc}0& 0& 0& 1\\ 3& 0& 0& 1\\ 0& 3& 0& 1\\ 0& 0& 3& 1\end{array}\right|=\frac{1}{6}\times 27=\frac{9}{2}$