`((1)/(2)x^(2)-(1)/(2)y^(2)+(1)/(4)z^(2))-((1)/(3)x^2+(1)/(4)y^(2)+(1)/(2)z^(2))+((1)/(4)x^(2)+(1)/(3)y^(2)+(1)/(3)z^(2))`

Solve : (1)/(2x)+(1)/(4y)-(1)/(3z)=(1)/(4),(1)/(x)=(1)/(3y),(1)/(x)-(1)/(5y)+(4)/(z)=2 (2)/(15)

If (x_(1),y_(1),z_(1)),(x_(2),y_(2),z_(2)) and (x_(3),y_(3),z_(3)) are the vertices of an equilateral triangle such that (x_(1)-2)^(2)+(y_(1)-3)^(2)+(z_(1)-4)^(2)=(x_(2)-2)^(2)+(y_(2)-3)^(2)+(z_(2)-4)^(2) =(x_(3)-2)^(2)+(y_(3)-3)^(2)+(z_(3)-4)^(2) then sum x_(1)+2sum y_(1)+3sum z_(1)

Which of the following line is passing through point of intersection of line (x-4)/(2)=(y-3)/(2)=(z-5)/(1) and the plane x+y+z=2( a) (x)/(2)=(y+1)/(3)=(z-3)/(4) (b) (x-2)/(3)=(y-1)/(3)=(z-2)/(2)(c)(x-2)/(2)=(y+1)/(3)=(z-2)/(4)(d)(x-2)/(2)=(y+1)/(3)=(z+3)/(4)

If (x_(1), y_(1), z_(1)), (x_(2), y_(2), z_(2)) and (x_(3), y_3), z_(3)) are the vertices of an equilateral triangle such that (x_(1)-2)^(2)+(y_(1)-3)^(2)+(z_(1)-4)^(2)=(x_(2)-2)^(2)+(y_(2)-3)^(2)+(z_(2)-4)^(2)=(x_(3)-2)^(3)+(y_(3)-3)^(2)+(z_(3)-4)^(2) then sum x_(1)+2sumy_(1)+3sum z_(1)=

Which of the following line is passing through point of intersection of line (x-4)/(2)=(y-3)/(2)=(z-5)/(1) and the plane x+y+z=2 (a) (x)/(2)=(y+1)/(3)=(z-3)/(4) (b) (x-2)/(3)=(y-1)/(3)=(z-3)/(2) (c) (x)/(2)=(y+1)/(3)=(z-2)/(4) (d) (x-2)/(2)=(y+1)/(3)=(z+3)/(4)

If xy+yz+zx=1 show that (x)/(1-x^(2))+(y)/(1-y^(2))+(z)/(1-z^(2))=(4xyz)/((1-x^(2))(1-y^(2))(1-z^(2)))

The value of |(2 y_(1)z_(1),y_(1) z_(2) + y_(2) z_(1),y_(1) z_(3) + y_(3) z_(1)),(y_(1) z_(2) y_(2) z_(1),2y_(2) z_(2),y_(2) z_(3) + y_(3) z_(2)),(y_(1) z_(3) + y_(3) z_(1),y_(2) z_(3) + y_(3) z_(2),2y_(3) z_(3))| , is

The value of |(2 y_(1)z_(1),y_(1) z_(2) + y_(2) z_(1),y_(1) z_(3) + y_(3) z_(1)),(y_(1) z_(2) y_(2) z_(1),2y_(2) z_(2),y_(2) z_(3) + y_(3) z_(2)),(y_(1) z_(3) + y_(3) z_(1),y_(2) z_(3) + y_(3) z_(2),2y_(3) z_(3))| , is