The value of `(x-y)(x+y)+(y-z)(y+z)+(z-x)(z+x) `is equal to

If the system of equations, 2x + 3y-z = 0, x + ky -2z = 0 " and " 2x-y+z = 0 has a non-trivial solution (x, y, z), then (x)/(y) + (y)/(z) + (z)/(x) + k is equal to

If x > y > z >0, then find the value of cot^(-1)(x y+1)/(x-y)+cot^(-1)(y z+1)/(z y-z)+cot^(-1)(z x+1)/(z-x)

If x > y > z >0, then find the value of cot^(-1)(x y+1)/(x-y)+cot^(-1)(y z+1)/(y-z)+cot^(-1)(z x+1)/(z-x)

|(0,xyz,x-z),(y-x,0,y-z),(z-x,z-y,0)| is equal to……………

|{:(x,4, y+z),(y,4,z+x),(z,4,x+y):}| is equal to:

If x , y ,z in [-1,1] such that cos^(-1)x+cos^1y+cos^(-1)z=3pi, then find the values of (1). x y+y z+z y and (2). x(y+z)+y(z+x)+z(x+y)

If x , y ,z in [-1,1] such that cos^(-1)x+cos^1y+cos^(-1)z=3pi, then find the values of (1) x y+y z+z y and (2) x(y+z)+y(z+x)+z(x+y)

If x , y ,z in [-1,1] such that cos^(-1)x+cos^1y+cos^(-1)z=3pi, then find the values of (1) x y+y z+z x and (2) x(y+z)+y(z+x)+z(x+y)

Let x,y,z in C satisfy |X| = 1,|y-6-8i| = 3 and |z + 1-7i| = 5 respectively, then the minimum value of |x-z| + |y-z| is equal to

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