Consider the following linear equations a x+b y+c z=0, b x+c y+a z=0, c x+a y+b z=0 Match the conditions/expressions in Column I with statements in Column II.

Step-by-step solution

Let = | array lll a & b & c b & c & a c & a & b array |=- 1 2 (a+b+c) [(a-b)^2+(b-c)^2+(c-a)^2 ] (A) If a+b+c 0 and a^2+b^2+c^2=a b+b c+c a =0 and a=b=c 0 The equations represents identical planes. (B) a+b+c=0 and a^2+b^2+c^2 a b+b c+c a =0 The equations have infinitely many solutions. array rlrl & & a x+b y & =(a+b) z & b x+c y & =(b+c) z & & (b^2-a c ) y & = (b^2-a c ) z y=z & a x+b y+c y & =0 & a x & =a y x=y=z array (C) a+b+c 0 and a^2+b^2+c^2 a b+b c+c a 0 The equation represent planes meeting at only one poin