Hey the answer is orthocentre option (2)
check that first of all, in all options u hav triangle ABC.....
so, keep it as fixed....
now, try for the positions of D...
the given equations imply that AD.BC=0 and BD.AC=0 (. means doy product)
so, AD and BC are perpendicular and so are BD and AC.....
for a given triangle ABC, this is possible only with the orthocentre.....
hope m clear...
thank u...
Goutham Harsha