Let |{:(y^(5)z^(6)(z^(3)-y^(3)),,x^(4)z^(6)(x^(3)-z^(3)),,x^(4)y^(5)(y^(3)-x^(3))),(y^(2)z^(3)(y^(6)-z^(6)),,xz^(3)(z^(6)-x^(6)) ,,xy^(2)(x^(6)-y^(6))),(y^(2)^(3)(z^(3)-y^(3)),,xz^(3)(x^(3)-z^(3)),,xy^(2)(y^(3)-x^(3))):}| " and " Delta_(2)= |{:(x,,y^(2),,z^(3)),(x^(4),,y^(5) ,,z^(6)),(x^(7),,y^(8),,z^(9)):}| .Then Delta_(1)Delta_(2) is equal to
If plane 2x+3y+6z+k=0 is tangent to the sphere x^(2)+y^(2)+z^(2)+2x-2y+2z-6=0 , then a value of k is
If A=({:(2,3,10),(4,-6,5),(6,9,-20):}) find A^(-1) . Using A^(-1) solve the system of equations. (2)/(x)+(3)/(y)+(10)/(z)=2,(4)/(x)-(6)/(y)+(5)/(z)=5,(6)/(x)+(9)/(y)+(20)/(z)=-4