uft x=b+c-2a, y=c+a-2b, z=a+b-2c

If x = b + c - 2a, y = c + a-2b , z = a + b-2c , then prove that x^3+y^3+z^3-3xyz=0

If x= b+c, y=c+a, z=a+b , then find the value of (x^2 + y^2 + z^2 -yz - zx-xy)/( a^(2) + b^(2) + c^(2) - bc - ca - ab)

If x = 6a + 8b + 9c, y = 2b - 3a - 6c and z = c - b + 3a, find : x - y +z

If x = 6a + 8b + 9c, y = 2b - 3a - 6c and z = c - b + 3a, find : x + y + z

Prove that |a x-b y-c z a y+b x c x+a z a y+b x b y-c z-a x b z+c y c x+a z b z+c y c z-a x-b y|=(x^2+y^2+z^2)(a^2+b^2+c^2)(a x+b y+c z)dot

Prove that |a x-b y-c z a y+b x c x+a z a y+b x b y-c z-a x b z+c y c x+a z b z+c y c z-a x-b y|=(x^2+y^2+z^2)(a^2+b^2+c^2)(a x+b y+c z)dot

Evaluate each of the following algebraic expressions for x=1,\ y=-1, z=2,\ a=-2,\ b=1,\ c=-2: (i) a x+b y+c z (ii) a x^2+b y^2-c z^2 (iii) a x y+b y z+c x y