If the straight line drawn through the point P3,2 and making an angle π6 with the x-axis meets the line 3x-4y+8=0 at Q, then the length of PQ is

The given line is 3x-4y+8=0             ---(1)Let PQ = r Then, the coordinates of Q are 3+rcosπ6,2+rsinπ6  or  3+32r,2+r2Since the point Q lies on the given line,∴    33+32r-42+r2+8=0⇒6+3r-16-4r+16=0 or  r=6Hence, PQ = 6