The value of `|[x+y,y+z,z+x],[z,x,y],[1,1,1]|` is

Use properties of determinants to evaluate : |{:(x+y,y+z,z+x),(z,x,y),(1,1,1):}|

If x^(2) + y^(2) + z^(2) = 1 . Then what is the value of |(1,z,-y),(-z,1,x),(y,-x,1)| ?

If x^(2)+y^(2)+z^(2)=1 , then what is the value of |{:(1,z,-y),(-z,1,x),(y,-x,1):}|= ?

If x+a=y+b+1=z+c then the value of [[x, (a+y), (a+x)], [y, (b+y), (b+y)], [z, (c+y), (c+z)]] is

Find the value of x,y, and z if : (i) [[3,x4,y]]=2.[[-1.5,1z,1]]

The values of x, y, z for the equations x-y+z=1, 2x-y=1, 3x+3y-4z=2 are

The value of x+y+z is 15 if a,x,y,z,b are in AP while 1/x+1/y+1/z is 5/3 if a,x,y,z,b are in HP ,then the value of a is

The value of ((x/y- y/x)(y/z -z/y) (z/x -x/z))/((1/x^(2) -1/y^(2))(1/y^(2)-1/z^(2))(1/z^(2)-1/x^(2))) is

Find the value of the "determinant" |{:(1,x,y+z),(1,y,z+x),(1,z,x+y):}|