The scalars l and m such that l→a+m→b=→c where →a,→b and →c are given vectors, are equal to
l=(→c×→b).(→a×→b)|→a×→b|2 ; m=(→c×→a).(→b×→a)|→b×→a|2
l→a+m→b=→c
(l→a+m→b)×→b=→c×→b⇒l→a×→b=→c×→b
Take dot product with →a×→b
⇒l|→a×→b|2=(→c×→b).(→a×→b)⇒l=(→c×→b).(→a×→b)|→a×→b|2
Similarly, m=(→c×→a).(→b×→a)|→b×→a|2