A CPR MU300 DIAMOND JET TURNS THE WRONG DIRECTION DURING RADAR VECTORING FOR AN ILS APCH TO RWY 5R AT DTW; MI.

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WHILE GETTING VECTORED FOR AN ILS RWY 5R AT YIP; APCH TOOK US ACROSS THE LOC (WE WERE FLYING NW). THERE WAS SOME DISCUSSION AMONG THE CREW ABOUT THE WAY ATC WAS GOING TO TURN US ON THE APCH. THEY DID NOT TELL US ABOUT XING THE LOC BUT WE NOTICED AND CONTINUED ON NW. THEY THEN TOLD US TO TURN (WE THOUGHT R) TO A 080 DEG HDG TOWARD THE FINAL. MY COPLT THOUGHT ATC SAID R TURN BUT IN THE TURN ATC SAID THEY GAVE US A L TURN. THEY SAID TO CONTINUE THE TURN AND VECTORED US FROM THE NW SIDE. WE HAD THOUGHT THEY WANTED A R TURN SINCE IT WAS A SHORTER TURN TO 080 DEGS. MOST CTLRS TELL A PLT THAT THEY ARE VECTORING THEM ACROSS THE LOC AND I THINK IT IS A GOOD IDEA. IT LETS THE PLT PLAN WHAT THE CTLR INTENDS TO DO. ALSO; I THINK THAT BESIDES TELLING A PLT WHICH DIRECTION TO TURN TO A HDG; A CTLR SHOULD EMPHASIZE THE DIRECTION OF TURN WHEN IT IS A SHORTER TURN THE OTHER WAY. SOME CTLRS DO THIS AND IT HELPS THE PLT (OR AT LEAST REINFORCES) TO TURN IN THE DIRECTION THE CTLR WISHES. AN EXAMPLE MIGHT BE 'TURN L 080 DEGS; A L TURN TO 080 DEGS.'