If `(a^2+b^2+c^2)(x^2+y^2+z^2)=(ax+by+cz)^2`, then show that `x:a=y:b=z:c`

If(a^(2)+b^(2)+c^(2))(x^(2)+y^(2)+z^(2))=(ax+by+cz)^(2) shewthatx :a=y:b=z:

If a^(2)+b^(2)+c^(2)=x^(2)+y^(2)+z^(2)=1, then show that ax+by+cz<1

If a^2+b^2+c^2 =16, x^2+y^2+z^2 = 25 and ax+by+cz = 20 , then show that (a+b+c) prop (x+y+z)

If a^2+b^2+c^2=x^2+y^2+z^2=1, then show that a x+b y+c z leq1.

If a^2+b^2+c^2=x^2+y^2+z^2=1, then show that a x+b y+c z leq1.

If (by+cz)/(b^2+c^2)=(cz+ax)/(c^2+a^2)=(ax+by)/(a^2+b^2) then prove that x/y=y/b=z/c

If a^(x)=b^(y)=c^(z) and b^(2)=ac, then show that y=(2zx)/(z+x)

If x^(2) : (by + cz) =y^(2) : (cz + ax) = z^(2) : (ax + by) = 1 , then show that a/(a+x) + b/(b+y) + c/(c+z) = 1 .

If x : a = y : b = z : c , then prove that (a^(2) + b^(2) + c^(2))(x^(2) + y^(2) + z^(2)) = (ax + by + cz)^(2)

If a^(2)+b^(2)+c^(2)=16,x^(2)+y^(2)+z^(2)=25 and ax+by+cz=20 then the value of (a+b+c)/(x+y+z)