Concept:The columns of the given determinant add up to a zero column, so its value is 0.Explanation:Let D=a−bb−cc−ap−qq−rr−px−yy−zz−x.Adding the three columns of D:(a−b+b−c+c−a,p−q+q−r+r−p,x−y+y−z+z−x)=(0,0,0).Thus, the columns are linearly dependent, so D=0.Given, D=kapxbqycrz,we get 0=k⋅det(second matrix).Hence, k=0.Answer:k=0