If `x+y+z=xyz` prove that `(2x)/(1-x^(2))+(2y)/(1-y^(2))+(2z)/(1-z^(2))=(2x)/(1-x^(2))(2y)/(1-y^(2))(2z)/(1-z^(2))`.

Prove that |(x^(2),x^(2)-(y-z)^(2),yz),(y^(2),y^(2)-(z-x)^(2),zx),(z^(2),z^(2)-(x-y)^(2),xy)|=(x-y)(y-z)(z-x)(x+y+z)(x^(2) + y^(2) + z^(2)) .

The angle between the lines (x-7)/(1)=(y+3)/(-5)=(z)/(3) and (2-x)/(-7)=(y)/(2)=(z+5)/(1) is equal to

If Q is the image of the point P (2,3,4) under the reflection in the plane x-2y+5z=6 then the equation of the line PQ is a) (x-2)/(-1)= (y-3)/2= (z-4)/5 b) (x-2)/(1)= (y-3)/(-2)= (z-4)/5 c) (x-2)/(-1)= (y-3)/(-2)= (z-4)/5 d) (x-2)/(1)= (y-3)/(2)= (z-4)/5

The equation of the plane through the point (2,-1,-3) and parallel to the lines (x-1)/(3)= (y+2)/(2)= ( z)/(-4) and ( x)/(2)= (y-1)/(-3) = (z-2)/(2) is

Prove that |(1,x,x^3),(1,y,y^3),(1,z,z^3)|=(x+y+z)(x-y)(y-z)(z-y) .

Delta_(1) = |(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)z^(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 a) Delta_(2)^(2) b) Delta_(2)^(3) c) Delta_(2)^(4) d)None of these