wsd110110
种子
共回答了20个问题采纳率：85% 举报
p表示α,q表示β：
|a+b|^2=(a+b)·(a+b)=|a|^2+|b|^2+2a·b=4+1+2(2cosp,2sinp)·(sinq,cosq)
=5+4(cospsinq+sinpcosq)=5+4sin(p+q),故：|a+b|^2∈[1,9],即：|a+b|的最小值是1
a·b=(2cosp,2sinp)·(sinq,cosq)=2sin(p+q)=3/5,条件不够,
另外c有什么用?
1年前
追问
8
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举报
wsd110110
b·c=(sinq,cosq)·(-1/2,sqrt(3)/2)=-sinq/2+sqrt(3)cosq/2=-sin(q-π/3)=3/5 即：sin(q-π/3)=-3/5，而：q∈(0,π)，故：q-π/3∈(-π/3,2π/3) 而：sin(q-π/3)=-3/5，故：q-π/3∈(-π/3,0]，故：cos(q-π/3)=4/5 sinq=sin(q-π/3+π/3)=sin(q-π/3)cos(π/3)+cos(q-π/3)sin(π/3) =(-3/5)*(1/2)+(4/5)*(sqrt(3)/2)=(4sqrt(3)-3)/10
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举报
wsd110110
b·c=(sinq,cosq)·(-1/2,sqrt(3)/2)=-sinq/2+sqrt(3)cosq/2=-sin(q-π/3)=3/5 即：sin(q-π/3)=-3/5，而：q∈(0,π)，故：q-π/3∈(-π/3,2π/3) 而：sin(q-π/3)=-3/5，故：q-π/3∈(-π/3,0]，故：cos(q-π/3)=4/5 sinq=sin(q-π/3+π/3)=sin(q-π/3)cos(π/3)+cos(q-π/3)sin(π/3) =(-3/5)*(1/2)+(4/5)*(sqrt(3)/2)=(4sqrt(3)-3)/10
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