if `Delta= |{:(3,,4,,5,,x),(4,,5,,6,,y),(5,,6,,7,,z),(x,,y,,z,,0):}|=0` then

If x,y,z, are in A.P., then value of the det A. where A=[(4,5,6,x),(5,6,7,y),(6,7,8,z),(x,y,z,0)] is :

If x, y , z are in A.P., then the value of the det (A) is , where A = [(4,5,6,x),(5,6,7,y),(6,7,8,z),(x,y,z,0)]

If x, y , z are in A.P., then the value of the det (A) is , where A = [(4,5,6,x),(5,6,7,y),(6,7,8,z),(x,y,z,0)]

Let |{:(y^(5)z^(6)(z^(3)-y^(3)),,x^(4)z^(6)(x^(3)-z^(3)),,x^(4)y^(5)(y^(3)-x^(3))),(y^(2)z^(3)(y^(6)-z^(6)),,xz^(3)(z^(6)-x^(6)) ,,xy^(2)(x^(6)-y^(6))),(y^(2)^(3)(z^(3)-y^(3)),,xz^(3)(x^(3)-z^(3)),,xy^(2)(y^(3)-x^(3))):}| " and " Delta_(2)= |{:(x,,y^(2),,z^(3)),(x^(4),,y^(5) ,,z^(6)),(x^(7),,y^(8),,z^(9)):}| .Then Delta_(1)Delta_(2) is equal to

Let |{:(y^(5)z^(6)(z^(3)-y^(3)),,x^(4)z^(6)(x^(3)-z^(3)),,x^(4)y^(5)(y^(3)-x^(3))),(y^(2)z^(3)(y^(6)-z^(6)),,xz^(3)(z^(6)-x^(6)) ,,xy^(2)(x^(6)-y^(6))),(y^(2)^(3)(z^(3)-y^(3)),,xz^(3)(x^(3)-z^(3)),,xy^(2)(y^(3)-x^(3))):}| " and " Delta_(2)= |{:(x,,y^(2),,z^(3)),(x^(4),,y^(5) ,,z^(6)),(x^(7),,y^(8),,z^(9)):}| .Then Delta_(1)Delta_(2) is equal to

Let |{:(y^(5)z^(6)(z^(3)-y^(3)),,x^(4)z^(6)(x^(3)-z^(3)),,x^(4)y^(5)(y^(3)-x^(3))),(y^(2)z^(3)(y^(6)-z^(6)),,xz^(3)(z^(6)-x^(6)) ,,xy^(2)(x^(6)-y^(6))),(y^(2)^(3)(z^(3)-y^(3)),,xz^(3)(x^(3)-z^(3)),,xy^(2)(y^(3)-x^(3))):}| " and " Delta_(2)= |{:(x,,y^(2),,z^(3)),(x^(4),,y^(5) ,,z^(6)),(x^(7),,y^(8),,z^(9)):}| .Then Delta_(1)Delta_(2) is equal to

Delta_(1) = |(y^(5)z^(6) (z^(3)-y^(3)),x^(4)z^(6)(x^(3)-z^(3)),x^(4)y^(5)(y^(3)-x^(3))),(y^(2)z^(3)(y^(6)-z^(6)),xz^(3)(z^(6)-x^(6)),xy^(2)(x^(6)-y^(6))),(y^(2)z^(3)(z^(3)-y^(3)),xz^(3)(x^(3)-z^(3)),xy^(2)(y^(3)-x^(3)))| and Delta_(2)=|(x,y^(2),z^(3)),(x^(4),y^(5),z^(6)),(x^(7), y^(8),z^(9))| Then Delta_(1) Delta_(2) is equal to a) Delta_(2)^(2) b) Delta_(2)^(3) c) Delta_(2)^(4) d)None of these

If X= [(2,3,0),(1,-1,5)] ,Y= [(-1,-2,3),(-1,0,2)] ,Z= [(0,4,-1),(5,6,-5)] find 3X+4Y-Z