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19:T14d2,まずベクトルの根本から理解しましょうか。
ベクトルとは 方向と大きさを兼ね備えた量のことを言います。 (1,2)と言われたら 大きさ 方向共にわかりますよね？
しかし！ 逆に言えば方向と大きさしかわかりません。 
宝探しに例えるならば ベクトルは
「南に4歩 西に3歩あるけ」という情報しか持ちません。 つまりはスタート(始点)が決まらなければ 宝の場所(終点)も分からないのです。
そこで出てくるのが位置ベクトルです。
位置ベクトルは始点を(0.0)に固定することで 終点を決めようというベクトルです。
より簡単にいうならば 原点(0,0)からある点(a,b)に行くためのベクトルのことを位置ベクトルと言います。
例えば 位置ベクトル(1,2)と言われたら 原点(0,0)からある点(1,2)にいくためのベクトルですよね？
つまり！お分かりだと思いますが 位置ベクトルの数値は座標の数値と同じになります。
なので 座標の計算で成り立つ公式は位置ベクトルでも成立します。
例えば 内分点の公式は内分ベクトルの公式と等しいですよね。
ここで頭がこんがらがりガチなポイントとしてvAB=vOB-vOAがあげられます。【ベクトルABをvectorの頭文字をとってvABと書きました。】
 ここで意識しなければならないのは 位置ベクトルは座標のように扱うことができるだけで本質的にはベクトルです。 
vAB=vOB-vOA=vOB vAO となり、AからOへ行くベクトルとOからBへ行くベクトルがあるので結果として AからBへ行くことができます。
ついてこれましたか？

次に ベクトルといえば内積(外積)が大事ですね。 これに関してもお話ししましょう。
ここにvAB=(a,b)とvCD=(c,d)があるとしましょう。
内積とはvAB•vCDの計算のことを言います。  具体的にいうならば vAB•vCD=ac bdですね。 そしてvAB•vCD=AB×CD×cos@ (@はABとCDのなす角です)も有名です。
しかしなんのことかさっぱりですよね？
詳しく説明していきます。
/vAB/^2=(vOB-vOA)^2=/vOB/^2 /vOA/^2-2OA•OBここまでは楽勝ですね。
ここで三角形OABを書いてみてください。
これ何かに似ていませんか？ そうです余弦定理です。余弦定理は
AB^2=OA^2 OB^2-2OA×OB×cos@です。 見比べてみると 2OA×OB×cos@=2OA•OBとなりませんか？ これこそが その不可解な等式のメカニズムです。
∴実は 外積は
vAB×vCD=ad-cb=AB×CD×sin@となります。 なので外積÷内積をすることでsin@/cos@=tan@などとすることもできます。わりと便利ですね。

長々とベクトルの話をしてきましたが、センターのベクトル問題で得点を取るための話をします。 ずばり一番重要なのは 内分公式の完ぺきな理解です。
MがABをt:sに内分するとすると
vOM=s vOA t vOB /s tが成立することは 内分点の公式から明らかです。
更にvOM=s/s t vOA   t/s t vOBと変形でき、係数の和が1になっていることをおさえておきましょう。
では 係数の和が1にならない時(内分 外分が成立していない時)  式に意味を持たせるためにはどうすればいいでしょうか。
具体例をだすと、
vON=2/3 vOA  2/5 vOBのとき、Nはどのような点でしょうか？
繰り返しになりますが、その点Nに意味を持つ意味を知るためには 係数の和が1になることが大切です。
なので例えば vON=3/5(10/9 vOA) 2/5 vOBと変形するとNは OQ=10/9 vOAを満たす点Qと点Bを2:3に内分する点とわかりますよね。

そしてもう一つ 発展させるとこれによって交点を求めることもできます。
例えば 点Tが直線ABと直線CDの交点であるとしましょう。 
このときTは線分AB上でかつ線分CD上ですね。  そしてここでポイントなのは 直線AB上にあるということはTは線分ABの内分点であるということ。 線分CDについても同様です。 しかし具体的に何対何かはわからないので、x:(1-x) 、y:(1-y)と仮定して立式してみます。
vOT=x vOA (1-x) vOB......㊀
vOT=y vOC (1-y) vOD......㊁です。
そしてその後の問題の流れとして想定されるのは vOCやvODをvOA vOBを用いて表すことができ、 それを㊁へ代入し、㊀と係数を比べます。 
具体的に
vOC=vOA vOB  vOD=2 vOA-3vOBと仮定して考えてみると、
㊁式はvOT=y(vOA vOB) (1-y)(2 vOA-3 vOB)=(y  2-2y) vOA  (y 3-3y) vOBとなりますね。
㊀と係数を比較すると
(y 2-2y)= x 
(y 3-3y)=(1-x)となり、x,yが求まり、それによってvOTが特定されます。


などなど 上記のことがしっかり完ぺきに理解できて入れば大体の問題はとけるのではないかなと思われます。
あとは面積公式などもありますが、それらは内積の式を考慮すれば必然的なことだとわかるはずです。
長くなってすいません。 頑張ってください。
∴誤字があればすいません。
1c:Tf9c,数学を根本的に理解する。
という勉強方法は、言葉で説明すると少し難しいので、ほんの少しだけここでやっていみたいと思います。


例えば、弧度法の中で「ラジアン」というのが出てくると思います。これは、「2π = 360°」を基準に考えよう。という風に習ったと思います。このラジアンを使って、扇形の弧の長さを求める公式で、「L = rθ」というのがあります。
皆さんの中に、この式を覚えているだけになっていて、意味を理解していない方はおられるでしょうか？

これは、小学校の時に習った、「円周の長さは2πr」というものを使っています。

どういうことかと言うと、「円を4分割した形である扇形のこの長さを求めよ。」という問題があった時、

小学校で習った式を使うと、求めるのは円周を4等分した長さなので、 ¼ × 2πr = ½πr

ラジアンを使って解くと、中心角 90° は、ラジアンでは ½π なので、L = r × ½π = ½πr 

よって、答えはどちらの式を使っても、½πr になりました。

中学の知識では、L = 2r × π × 角度 / 360°
高校数学では、L = rθ
どちらの公式でも求められますが、公式で見ると、弧度法を使った方が分かりやすいですよね。



という感じです。

公式をただ覚えるだけでなく、意味を理解しながら使えるようになる。ということが、根本的に理解するということになります。

先程の例で言うと、ラジアンというものはどういう意味を持つのか。ラジアンを使えるようになると、計算がどう変わるのか。というのを理解しておく必要があります。



これは、ほかの公式でも当てはまります。

例えば、加法定理の公式：
sin(a+b) = sin(a)cos(b) + cos(a)sin(b)
これを使って2倍角の公式を作ります。
sin2a = sin(a+a) = sin(a)cos(a) + cos(a)sin(a)
          = 2sin(a)cos(a)


例えば、等差数列の和の公式：
S = ½n(a + l) (a：初項、l：末項、n：項数)
これに、末項：l = a + (n - 1)d (d：交差) を代入すると、
S = ½n(2a + (n - 1)d)
これが教科書に乗っている和の公式の2つになります。


こんなん知ってるよ。という方もいるかもしれません。ただ、これが数学を根本的に理解するということになります。

もう少し難しい話に行くと、
・解の公式ってなんであの形なの？
・平方完成ってなんでするの？
・円の方程式の意味は？
・微分と積分の関係は？
・ベクトルって何？
などなど……
キリがないので、この辺りにしておきますが、




要するに、公式の意味を理解することで、数学を本質的に理解しよう。という訳です。

しかも、これらは全てほとんどの教科書に載っています。理解しようと思うと、教科書を読めば大体のことが分かります。


数学を根本的に理解すると、問題を解くときに答え方がパッと思いつきやすくなると思います。さらに、公式の丸暗記では、時間が経つと忘れてしまうかもしれませんが、理論的に覚えていると、脳の構造的にも忘れにくくなるということもあります。なので、この勉強方法をオススメする方はたくさんいますし、私もこのやり方で勉強しました。

ただ、人によっては向き不向きがありますので、これを絶対に使った方がいいとは私は言えません。

実際に、私もこれで苦手だった数学が、だんだんと解けるようになったので、興味があれば、是非やってみてください。

長文失礼しました。是非参考になればと思います。2:["$","main",null,{"className":"px-4 pt-4 pb-4","children":["$","div",null,{"className":"max-w-3xl mx-auto w-full","children":[["$","div",null,{"className":"mb-8","children":["$","$L7",null,{"href":"https://unilink-app.onelink.me/isbO/h6xeh63x?advice=ilHZKYOfiHRc1bK4rehk","target":"_blank","children":["$","$L8",null,{"src":"/images/web_to_app_banner.jpg","width":3660,"height":1500,"sizes":"100vw","style":{"width":"100%","height":"auto"},"alt":"UniLink WebToAppバナー画像","className":"mb-4 rounded"}]}]}],["$","h1",null,{"className":"text-xl font-semibold mb-2","children":"対数の計算"}],["$","div",null,{"className":"flex justify-between mb-4","children":[["$","div",null,{"className":"text-left text-xs text-caption","children":["クリップ(",0,") コメント(",0,")"]}],["$","div",null,{"className":"text-right text-xs text-caption","children":"9/13 8:48"}]]}],["$","div",null,{"className":"coach-mark 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items-center py-4","children":[["$","div",null,{"className":"flex-1 mr-3","children":[["$","div",null,{"className":"mb-1","children":"A方式かB方式か"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"慶應経済学部の者です。\n\n先に僕の意見を述べますと、自分が得意な方の受験科目で受けた方がいいと思います。ですが、数学と世界史の出来具合が同じだった場合の話をさせていただきます。\n\nその場合はA方式の方がいいと思います。理由はいくつかありますが、主な２つを紹介します。まず１つ目、A方式は足切りラインが英数のマーク部分の合計であり、足切りラインが英語のみのB方式に比べ足切りを喰らいにくいからです。英語の長文をミスったらアウトのB方式に比べるとだいぶ気持ちが楽になると思います。次に２つ目、合格者数が違うからです。A方式はB方式の2倍ほどの合格者数を出しています。もちろんその分A方式の方が受験者は多いですが、倍率はA方式の方が低くなります。また、補欠合格者の数は圧倒的にA方式の方が多いです。\n\n以上のような理由から僕はA方式受験をオススメします。しかし、理系からの受験者が少なからずa方式にはいます。そのため数学の出来はそこそこよくなければいけません。過去問を解いてみて自分がいけそうだと思える方式で受験しましょう。"}],["$","div",null,{"className":"flex mb-1","children":[["$","svg",null,{"stroke":"currentColor","fill":"currentColor","strokeWidth":"0","viewBox":"0 0 24 24","className":"text-subPrimary mr-1","children":["$undefined",[["$","path","0",{"fill":"none","d":"M0 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items-center py-4","children":[["$","div",null,{"className":"flex-1 mr-3","children":[["$","div",null,{"className":"mb-1","children":"慶應 経済 A方式の入試について"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"私も理系で、結局理工学部に進学しましたが、経済学部A方式も受けました。結果は補欠合格だったので、参考になるかわかりませんが、解答します。\n私の場合は実は国立を目指していましたが、受験期後半はだれてしまって、正直本気で目指していたと言えなかったと思います。\n\nまず結論から言えば可能だと思います。確か、英語、小論文、数学ですよね？\n数学は理系であれば受験勉強をしていれば大丈夫でしょう。\n英語はやはり慶應なので難しかったと思いますが、これも他の科目と同様に受験勉強をしっかりして、英語が得意科目であれば大丈夫です。過去問で対策するとよいと思います。\n小論文については、私は特別な対策はしませんでしたが、新聞を読んでいると構想が練りやすいと思います。わたしの場合はそのころ読んだ記事を思い出して、偶然上手くつなげられたのでそこから広げました。朝だけでも軽く新聞を読むといいかもしれないです。\n国語が好きだと答えやすいでしょう。現代文をたまにといておくといいです。\n受験のときの私に似ていたので回答させていただきました。参考になれば幸いです。\n"}],["$","div",null,{"className":"flex mb-1","children":[["$","svg",null,{"stroke":"currentColor","fill":"currentColor","strokeWidth":"0","viewBox":"0 0 24 24","className":"text-subPrimary mr-1","children":["$undefined",[["$","path","0",{"fill":"none","d":"M0 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