STATEMENT-1 : If `a, b, c` are distinct and `x, y, z` are not all zero and `ax + by + cz = 0, bx + cy + az = 0, cx + ay + bz = 0`, then `a + b + c = 0` and STATEMENT-2 : `a^2 + b^2 + c^2 > ab + bc + ca`, if `a, b, c` are distinct.

Options

A. Statement - 1 is True, Statement-2 is True, Statemen-2 is a correct explanation for Statement - 1
B. Statement - 1 is True, Statement - 2 is True, Statement - 2 is Not a correct explanation for Statement - 1
C. Statement - 1 is True, Statement - 21 is False
D. Statement - 1 is False, Statement - 1 is True

Explanation

`because" "Delta=|{:(a,b,c),(b,c,a),(c,a,b):}|=-{a^3+b^3+c^3-3abc}`
`:." "Delta=-(a+b+c){a^2+b^2+c^2-ab-bc-ca}=0`
`[because" "a+b=c=0]" "["Non-Trivial"]" and "a^2+b^2+c^2-ab-bc-ca`
`=1/2[(a-b)^2+(b-c)^2+(c-a)^2]gt0`
Hence, option (1) is correct.