數學vector

Suppose the position vectors of points X and Y are x and y respectively. Z is a point on XY with a position vector z=mx+ny. Given that m+n=1.Let x=i+4j,y=2i-j and the angle between OY and OZ is 30度. I have already proved that 239m^2+20mn-25n^2=0 and 194m^2+70m-25=0 . A and B are two points on the line XY such that OA and OB make 30度 with OY. Find OA.OB