Let `vec(a),vec(b),vec(c)` be three unit vectors and `vec(a)*vec(b)=vec(a)*vec(c)=0` . If the angle between `vec(b)` and `vec(c)` is `(pi)/(3)` then find the value of `|[vec(a)vec(b)vec(c)]|` .

Answer

`(sqrt(3))/(2)`