A plane is parallel to two lines direction ratios are (1,0,-1) and (-1,1,0) and it contains the point (1,1,1) . If it cuts the co-ordinate axes at A, B, C, then the volume of the tetrahedron OABC is cu. units.

Step-by-step solution

Direction ration of normal to the plane can be obtained by aligned & a 0 0-1 (-1) = b (-1) (-1)-1 0 = c 1 1-(-1) 0 & a , b , c 1,1,1 aligned Hence equation of the plane 1(x-1)+1(y-1)+1(z-1)=0 aligned & x+y+z=3 & x 3 + y 3 + z 3 =1 aligned The plane intersects the co-ordinate axes at (3,0,0),(0,3,0) and (0,0,3) Hence, volume of tetrahedron OABC is