Given that `vec(a)=vec(i)+vec(j) +vec(k), vec(b)=vec(i)-vec(j)+vec(k), vec(c)=vec(i)+vec(j)-vec(c)=vec(i)+vec(j)-vec(k)` , the value of `(vec(a).vec(b))+(vec(b).vec(c))+(vec(c).vec(a))` is ______?

Answer

1

Explanation

`(1-1+1)+(1-1-1)+(1+1-1)=1-1+1=1`