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Mathematics Senior High

なぜOH=sa+tbとしてるんですか?

p 基本 例題 25 垂心の位置ベクトル 平面上に△OAB があり、OA=5,OB=6, AB=7 とする。 また, △OABの垂 00000 心をHとする。 (1) COS ∠AOB を求めよ。 (2) OA= a, OB = とするとき, OH を a, 1 を用いて表せ。 指針 三角形の垂心とは, 三角形の各頂点から対辺またはその延長に下ろした垂線の交点であり, 解答 △OABの垂心Hに対して, OA⊥BH, OBIAH, ABIOH が成り立つ。 そこで, OA⊥BH といった図形の条件をベクトルの条件に 直して解く。 (2) では OH = sa+t とし, OA・BH=0, OB・AH=0 の2つの条件から,s,tの値を求める。 (1) 余弦定理から EDU COS ∠AOB= OA⊥BH より OA・BH=0 である から よって ゆえに 25s+6(t-1)=0 すなわち 25s+6t=6 ① また, OB ⊥AHよりOB・AH = 0 であるから {(s-1)a+t}=0 (s-1)ã·6+t|b²=0 したがって (2) (1) 5 à·b=|ā||5|cos <AOB=5.6.-= -=6 △OAB は直角三角形でないから,垂心Hは2点A,Bと 一致することはない。 F 21-9 Hは垂心であるから OA⊥BH, OB⊥AH OH = sa + to (s,t は実数)とする。 A+8A CHORUSS 0 52 +62-72 2・5・6 S= a•{sa+(t-1)}=0 tsasaH slal²+(t-1)ã·b=0C=100 よって ゆえに 6(s-1)+36t=0 すなわち s+6t=1 19 ① ② から 1)-(2*4 144 5 24' OH= 12 1 60 5 t= A 5 → 2ä+ 196 a+ 24 144 = p.400 基本事項 ⑤ 631 B ------ A stronas 重要 28 [参考] AB=18- =161²-26-a+la1² H |AB|=7, |a|=5, ||=6で あるから 72=62-2 ・a +5² よって 1=6 18-TA ①垂直→ (内積) = 0 BH = OH-OB O |a| =5, a-6=6 ①垂直→ (内積) = 0 ■AH=OH-OA A HA①-②から 24s=5 HA& 2a-6-6, 161=63 3x+u+= B 421 4 位置ベクトル、ベクトルと図形 X

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English Senior High

至急よろしくお願いします😭😭できれば今日のお昼までに答えてくださる方を待っています>< 英検2級の過去問です。(28)の答えが4なのですが、なぜそうなるのかわかりません、、どういった経緯で3人とわかるのか詳しく教えていただきたいです🙇🏻‍♀️ また、赤線部分のjoin ... Read More

From: Amy Gordon To: All Customer Service Staff <customerservicestaff@g-kelectronics.com> Date: January 23 Subject: Staff changes <a.gordon@g-kelectronics.com> Dear Customer Service Staff, I hope everyone enjoyed themselves at the company party last Friday. I had a really good time. I think that the Grand Hotel was the perfect place to have it. Don't forget that some of you won prizes in the bingo games that we played. Steve Miller in the sales department says that he has the prizes, so if you won something, go and see him to pick up your prize. I have some other announcements as well today. Six new people will be joining our company next month. They've all recently graduated from college, and two of them will be coming to work with us in the customer service department. We'll have three new co-workers altogether because Kent Gardiner will also be moving to our department at the same time. He has worked in the design department at G&K Electronics for 10 years, so I'm sure that many of you already know him. There are a couple of other staff changes, too. Peter Smith, the manager of the accounting department, will be retiring at the end of next month. Peter has worked at G&K Electronics for over 40 years. There will be a short retirement ceremony for him in Meeting Room A at 5 p.m. on February 28. Also, starting next week, Rachel Martin will take six months off because her baby will be born very soon. Sincerely, Amy Gordon Customer Service Department Manager

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