Let the equation of the plane through (2,2,2) be a(x−2)+b(y−2)+c(z−2)=0 Since, it is parallel to the straight lines having Dr's (1,0,−1) and (−1,1,0), therefore a−c=0 and −a+b=0 ⇒a=b=c Therefore, equation of plane is x−2+y−2+z−2=0 x+y+z=6⇒
x
6
+
y
6
+
z
6
=1 Its intercepts on coordinate axes are A(6,0,0),B(0,6,0) and C(0,0,6). Hence, the volume of tetrahedron OABC =