If a= x y-z , b= y z-x and c= z x-y , where x, y and z are not all zero, then what is the value of a b+b c+c a= ?

Step-by-step solution

We have, a= x y-z , b= y z-x , c= z x-y where, x, y, z 0 Put x=1, y=2 and z=3 aligned & a= 1 2-3 =-1 & b= 2 3-1 =1 & c= 3 1-2 =-3 aligned Now, a b+b c+c a=-1-3+3=-1 a b+b c+c a=-1