If `y+1/z=1` and `x+1/y=1` , then what is the value of `x y z` ? `-1` (b) 0 (c) `1/2` (d) 1

If x + y + z = 400 and x : y : z = 1 : 1 : 2 , then what is the value of z ?

If a^(x)=b, b^(y)=c, c^(z)=a , then what is the value of (1)/((xy+yz+zx))((1)/(x)+(1)/(y)+(1)/(z)) ?

If x^(2)+y^(2)+z^(2)=1 , then what is the value of |{:(1,z,-y),(-z,1,x),(y,-x,1):}|= ?

If x+y+z=0 then what is the value of (1)/(x^(2)+y^(2)-z^(2)) +(1)/(y^(2)+z^(2)-x^(2)) +(1)/(z^(2)+x^(2)-y^(2)) ?