已知向量AB=3i -7j, BC=i – 3j, OC 与AC反向且|OC|=3/4|AC|,求点C的坐标
题目
已知向量AB=3i -7j, BC=i – 3j, OC 与AC反向且|OC|=3/4|AC|,求点C的坐标
答案
向量AC=AB+BC=3I-7j +i-3j=4i-10j
因为向量OC与向量AC反向共线,
设：OC=λAC(λ<0)
|OC|=|λ||AC|
|OC|= - λ|AC|
(3/4)|OC|= - λ|AC|
λ= - 3/4
向量OC= - (3/4)(4I-10j)= -3i +(15/2) j
所以,
C(-3,15/2)
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