[解題] 高二數學向量
1.年級：高二
2.科目：數學
3.章節：向量
4.題目： __ __ __
設K為三角形ABC外心 , AB=4 , BC=根號21 , CA=5 , 直線AK交
__ → → →
BC於D點 , 若AD=rAB+sAC , 求數對(r,s)
5.想法：
→ → →
假設 AK=aAB+bAC
→ → → → →
AK AB = a|AB|^2 + b AC AB 8=16a+10b
→ → → → → =>
AK AC = a AB AC + b|AC|^2 25/2=10a+25b
解出 a=1/4 , b=2/5
→ → → →
再令 AD = tAK = (t/4)AB+(2t/5)AC , 因為 B-D-C 解出 t=20/13
→ → →
則 AD = 5/13 AB + 8/13 AC
不知道算法哪裡有問題？解答答案為：(3/11,8/11)
題庫抓的考古題有解析 , tanθ那一行開始看不懂 http://0rz.tw/hSxon
註：雄女96學年度二上第一次段考 計算證明第一題
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