1. Today’s Math Question 2009 11 15
0005
( ) ( )
4 5 2 4
O A , , B (1, 2) , C , , D (3, 1)
3 3 3 3
−→ −→ −
−→ −→
P (x, y) OP = lOA + mOB + nOC (l + m + n = 2, l 0, m 0)
(1) P
(2) (1) D

2. Today’s Math Answer
0005
−→ (2) H (a, b) D CA
(1) OP
−→ −→ −
−→ −→
OP lOA + mOB nOC − → −→
−
= + −
l+m l+m l+m C A · DH = 0
4 2
AB m:l Q (a − 3) + (b − 1) = 0 (1)
3 3
−→ −→
OP − → nOC 1
= OQ + H C A (y = x + 2)
l+m l+m 2
−→ −→ − →
OP = (l + m)OQ + nOC 1
−→ −→ −→ b= a+2 (2)
OP (l + m)OQ + nOC 2
=
l+m+n (l + m) + n
(1) (2)
QC n : (l+m) R l+m+n =
a = 2, b = 3 H (2, 3) . . . . . .
2
−→
OP −→
= OR
2
−→ −→
OP = 2OR
( ) ( )
8 10 4 8
A , , B (2, 4) , C ,
3 3 3 3
ABC BC
......