If a b c 0 and the system of equations x+7 a y+2 a z=0, x+6 b y+2 b z=0 , x+5 c y+2 c z=0 has a non-trivial solution, then a, b, c are in

Step-by-step solution

Given, system of linear equation, a b c 0 , is x+7 a y+2 a z=0, x+6 b y+2 b z=0 and x+5 c y+2 c z=0 has a non-zero trivial solution. aligned & So, A=0 | array ccc 1 & 7 a & 2 a 1 & 6 b & 2 b 1 & 5 c & 2 c array |=0 & 1(12 b c-10 b c)-7 a(2 c-2 b)+2 a(5 c-6 b)=0 & 2 b c-4 a c+2 a b=0 & 2 a c=b c+a b & b= 2 a c a+c or 2 b = 1 a + 1 c aligned Then, a, b, c are in Harmonic Progression. Hence, option (a) is correct.