Let S be the set of all real values of such that a plane passing through the points (- ^2, 1,1 ), (1,- ^2, 1 ) and (1,1,- ^2 ) also passes through the point (-1,-1,1) . Then S is equal to

Step-by-step solution

from the condition of coplanarity of four points aligned & | array ccc - ^2+1 & 1+1 & 1-1 1+1 & - ^2+1 & 1-1 1+1 & 1+1 & - ^2-1 array |=0 & | array ccc - ^2+1 & 2 & 0 2 & - ^2+1 & 0 2 & 2 & - ^2-1 array |=0 & (- ^2-1 ) (- ^2+1 )^2-4 =0 & - ^2=1,- ^2+1=2 or - ^2+1=-2 & ^2=-1 or ^2=3 & = 3 [ ^2=-1 not possible ] & aligned