Amaths向量

(a) From the given, we have:
OC = (k + 1)i.
So by the point of division formula:
OD = (2OB + OC)/(2 + 1)
= (1/3)[2j + (k + 1)i]
= [(k + 1)i]/3 + 2j/3
(b)(i) Since OD is a unit vector, |OD| = 1
(k + 1)2/9 + 4/9 = 1
(k + 1)2 + 4 = 9
k + 1 = √5 since k > 0
k = √5 - 1
(ii) cos ∠BOD = (OB . OD)/|OB||OD|
= OB . OD since |OB| = |OD| = 1
= 2/3
∠BOD = 48

2008-09-10 22:23:09 補充：
粗字體的表示 vector quantities

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