`(x)/(z)=(1)/(3)`
If in the equation above x and z are integers which are possible values of `(x^(2))/(z)`?
I.`(1)/(9)`
II.`(1)/(3)`
III. 3

(i) Find the equations of the straight line passing through the point (2,3,-1) and is perpendicular to the lines : ( x-2)/(2) = (y + 1)/(1) = (z - 3)/(-3) and (x - 3)/(1) = (y + 2)/(1) = (z - 1)/(1) . (ii) Find the equation of the line which intersects the lines : (x + 2)/(1) = (y - 3)/(2) = (z + 1)/(4) and (x - 1)/(2) = (y - 2)/(3) = (z - 3)/(4) Perpendicular and passes through the point (1,1,1) .

The system of equations 3x+y+2z=6,xyz=-5,3xy+2yz+6xz=-1 has a solution (x,y,z), where x,y,z are integers.Then the value of (x+z)/(y) is equal to (i)0(ii)1(iii)2(iv)3

If x=3, y=2 and z=-1 , then the value of (x^3+y^3+1)/(y^3-z^3) is

If ((1)/(x)) + ((1)/(y)) + ((1)/(z)) = 0 and x + y + z = 9 , what is the value of x^(3) + y^(3) + z^(3) - 3xyz ?

The value of {(x-y)^3+(y-z)^3+(z-x)^3}/{9(x-y)(y-z)(z-x)} (1) 0 (2) 1/9 (3) 1/3 (4) 1

Without expanding as far as possible, prove that |{:(1,1,1),(x,y,z),(x^(3),y^(3),z^(3)):}| = (x-y)(y-z)(z-x)(x+y+z) .

Without expanding as far as possible, prove that |{:(1,1,1),(x,y,z),(x^(3),y^(3),z^(3)):}| = (x-y)(y-z)(z-x)(x+y+z) .

If x = 1, y = - 2 and z = 3. find the value of (i) x^(3) + y^(3) + z^3-3xyz (ii) 3xy^(4) - 15 x^(2) y + 4z

If sin^-1x + sin^-1 y + sin^-1z = (3pi)/2, then the value of x^9 + y^9 + z^9 - (1)/(x^9y^9z^9) is equal to