complex vector

(a)
OA.OB=3-m
OA.OB
=|OA||OB|cos angle AOB
=(√10)(√(1+m^2))(-1/√5)
=-√[2(1+m^2)]

So
3-m=-√[2(1+m^2)]
m-3=√[2(1+m^2)]
(m-3)^2=2+2m^2
m^2-6m+9=2+2m^2
m^2+6m-7=0
(m+7)(m-1)=0
m=1 or -7

Since m<0 we have m=-7

(b)

OA.OB=3-m=3+7=10

It is because in this case, the question choose the wrong angle (obtuse angle ) rather than the correct one acute angle

2008-05-13 00:19:10 補充：
照我想來﹐條math是大學生出來給大學生玩的。有點教壞中學生之嫌。因為故意用隻錯的角

2008-05-13 00:20:02 補充：
你畫個圖知道OA去OB﹐逆時針的話是acute angle

2008-05-13 14:35:07 補充：
應該說明個隻鈍角是順時針計的