`x+y+z=x y z ,\ t h e n`

If a ,\ b ,\ c >0\ a n d\ x ,\ y ,\ z in R , then the determinant |\ \ (a^x+a^x)^2(a^x-a^(-x))^2 1(b^y+b^(-y))^2(b^y-b^(-y))^2 1(c^z+c^(-z))^2(c^z-c^(-z))^2 1| is equal to- a. a^x b^y c^x b. a^(-x)b^(-y)c^(-z)\ c. a^(2x)b^(2y)c^(2x) d. zero

If y z+z x+x y=12 ,w h e r ex ,y ,z are positive values, find the greatest value of x y zdot

If the system of linear equations x+a y+a z=0,\ x+b y+b z=0,\ x+c y+c z=0 has a non zero solution then System is always non trivial solutions System is consistent only when a=b=c If a!=b!=c then x=0,\ y=t ,\ z=-t\ AAt in R If a=b=c\ t h e n\ y=t_1, z=t_2,\ x=-a(t_1+t_2)AAt_1, t_2 in R

If the lattice point P(x, y, z) , x, y, zgto and x, y, zinI with least value of z such that the 'p' lies on the planes 7x+6y+2z=272 and x-y+z=16, then the value of (x+y+z-42) is equal to

If x > 0, y > 0, z>0 and x + y + z = 1 then the minimum value of x/(2-x)+y/(2-y)+z/(2-z) is

For positive numbers x ,\ y\ a n d\ z the numerical value of the determinant |1(log)_x y(log)_x z(log)_y x1(log)_y z(log)_z x(log)_z y1| is- a. 0 b. logx y z c. "log"(x+y+z) d. logx\ logy\ logz

Consider the lines x=y=z and line 2x+y+z-1=0=3x+y+2z-2 , then

If x^2+y^2+z^2=r^2,t h e ntan^(-1)((z y)/(x r))+tan^(-1)((x z)/(y r))+tan^(-1)((x y)/(z r)) is equal to pi (b) pi/2 (c) 0 (d) none of these

If Delta = abs{:(x+y+z^(2) , x^(2) + y+ z, x+y^(2) + z),(z^2, x^2, y^2),(x+y,y+z,x+z):} , (where ( x ne y ne z) x, y, z in R- {0} ) then Delta= ........