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|[x,a,x+a],[y,b,y+b],[z,c,z+c]|=0...

`|[x,a,x+a],[y,b,y+b],[z,c,z+c]|=0`

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Show without expanding at any stage that: [x,a,x+a],[y,b,y+b],[z,c,z+c]|=0

Using the property of determinants and without expanding {:[( x,a,x+a),( y,b,y+b),(z,c,z+c)]:} =0

Using the property of determinants and without expanding {:[( x,a,x+a),( y,b,y+b),(z,c,z+c)]:} =0

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+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

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

If |[x+a, y+b, z+c] , [y+b, z+c, x+A] , [z+c, x+a, y+b]|=0 and a+c=-b then x,-y/2,z are in (A) A.P. (B) G.P. (C) H.P. (D) None of these

If x ,y ,z are different from zero and "Delta"=|[a, b-y ,c-z],[ a-x, b ,c-z],[ a-x, b-y, c]|=0, then the value of the expression a/x+b/y+c/z is a. 0 b. -1 c. 1 d. 2

If x ,y ,z are different from zero and "Delta"=|[a, b-y ,c-z],[ a-x, b ,c-z],[ a-x, b-y, c]|=0, then the value of the expression a/x+b/y+c/z is a. 0 b. -1 c. 1 d. 2