Home
Class 12
MATHS
STATEMENT-1 : If a, b, c are distinct an...

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.

Promotional Banner

Similar Questions

Explore conceptually related problems

If x, y, z are not all zero & if ax + by + cz=0, bx+ cy + az=0 & cx + ay + bz = 0 , then prove that x: y : z = 1 : 1 : 1 OR 1 :omega:omega^2 OR 1:omega^2:omega , where omega is one ofthe complex cube root of unity.

If x, y, z are not all zero & if ax + by + cz=0, bx+ cy + az=0 & cx + ay + bz = 0 , then prove that x: y : z = 1 : 1 : 1 OR 1 :omega:omega^2 OR 1:omega^2:omega , where omega is one ofthe complex cube root of unity.

If x, y, z are not all zero & if ax + by + cz=0, bx+ cy + az=0 & cx + ay + bz = 0 , then prove that x: y : z = 1 : 1 : 1 OR 1 :omega:omega^2 OR 1:omega^2:omega , where omega is one ofthe complex cube root of unity.

Consider the following linear equations ax+by+cz=0,bx+cy+az=0,cx+ay+bz=0

if a gt b gt c and the system of equations ax + by + cz = 0, bx + cy + az 0 and cx + ay + bz = 0 has a non-trivial solution, then the quadratic equation ax^(2) + bx + c =0 has

if a gt b gt c and the system of equations ax + by + cz = 0, bx + cy + az 0 and cx + ay + bz = 0 has a non-trivial solution, then the quadratic equation ax^(2) + bx + c =0 has

Consider the system of equations ax + by + cz = 2 bx + cy + az = 2 cx + ay + bz = 2 where a,b,c are real numbers such that a + b + c = 0. Then the system