If `x+y+z=0` , prove that `|[xa, yb,zc],[yc, za, xb], [zb, xc, ya]|=x y z|[a, b, c],[c ,a, b],[b ,c,c]|`

If x+y+z=0 prove that |[a x, b y, c z],[ c y, a z ,b x],[ b z ,c x ,a y]|=x y z|[a, b, c],[c ,a ,b],[b ,c ,a]|

If x+y+z=0 prove that |[a x, b y, c z],[ c y, a z ,b x],[ b z ,c x ,a y]|=x y z|[a, b, c],[c ,a ,b],[b ,c ,a]|

If x+y+z=0 prove that | xa yb zc yc za xb zb xc ya y|=x y z|a b c c a b b c a|

If x+y+z = 0 prove that |{:(xa,yb,zc),(yc,za,xb),(zb,xc,ya):}|=xyz|{:(a,b,c),(c,a,b),(b,c,a):}|

If x+y+z=0=a+b+c, then |{:(xa,yb,zc),(yc,za,xb),(zb,xc,ya):}|=

If x+y+z=0 prove that |a x b y c z c y a z b x b z c x a y|=x y z|a b cc a bb c a|

If x+y+z=0=a+b+c, then |{:(xa,yd,zc),(yc,za,xb),(zb,xc,ya):}|=

Prove that |(x+2a,y+2b,z+2c),(x,y,z),(a,b,c)|=0

If x+y+z=0 and |(xa, yb, zc),(yc,za, xb),(zb,xc, ya)|=k|(a,b,c),(b,c,a),(c,a,b)| then k =

prove that abs[[a,b,c],[a+2x,b+2y,c+2z],[x,y,z]]=0