If `|(x,y,z),(-x,y,z),(x,-y,z)|=k xyz`, then `k=`

If ([y+z,x,yz+x,z,xx+y,y,z])=k(x-z)^(2), then find K

Without expanding, prove the following |(x,y,z),(x^2,y^2,z^2),(x^3,y^3,z^3)|=xyz(x-y)(y-z)(z-x)

The value of |(x+y,y+z,z+x),(x,y,z),(x-y,y-z,z-x)|=

If |(x+y,y+z,z+x),(y+z, z+x,x+y),(z+x,x+y,y+z)| =k |(x,z,y),(y,x,z),(z,y,x)| , then k is equal to

If |(x+y,y+z,z+x),(y+z, z+x,x+y),(z+x,x+y,y+z)| =k |(x,z,y),(y,x,z),(z,y,x)| , then k is equal to

Prove that: {:|(x,y,z),(x^2,y^2,z^2),(x^3,y^3,z^3)|=|(x,x^2,x^3),(y,y^2,y^3),(z,z^2,z^3)| = xyz(x-y(y-z)(z-x)

Value of |(x+y,z,z),(x,y+z,x),(y,y,z+x)| where x , y ,z are non - zero real number is equal to a)xyz b)2xyz c)3xyz d)4xyz

If xyz=m and det p=|{:(x,y,z),(z,x,y),(y,z,x):}| , where p is an orthogonal matrix. If y=x=z, then z is equal to

If xyz=m and det p=|{:(x,y,z),(z,x,y),(y,z,x):}| , where p is an orthogonal matrix. If y=x=z, then z is equal to