सिद्ध कीजिए कि:
`|(x,y,z),(-x,y,z),(-x,-y,z)|=4xyz.`

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

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

|{:(0,xyz,x-z),(y-x,0,y-z),(z-x,z-y,0):}|=".........."

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)

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)

prove that: |(y+z,z,y),(z,z+x,x),(y,x,x+y)|=4xyz

prove that: |(y+z,z,y),(z,z+x,x),(y,x,x+y)|=4xyz

Prove: |(z, x, y),( z^2,x^2,y^2),(z^4,x^4,y^4)|=|(x, y, z),( x^2,y^2,z^2),(x^4,y^4,z^4)|=|(x^2,y^2,z^2),(x^4,y^4,z^4),(x, y, z)|=x y z(x-y)(y-z)(z-x)(x+y+z) .

Show that |(x,y,z),(x^(2),y^(2),z^(2)),(x^(3),y^(3),z^(3))|=xyz (x-y) (y-z) (z-x)