{"id":1623,"date":"2024-05-27T15:42:10","date_gmt":"2024-05-27T06:42:10","guid":{"rendered":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/?p=1623"},"modified":"2024-06-26T15:41:42","modified_gmt":"2024-06-26T06:41:42","slug":"top-math2-2q2h-1","status":"publish","type":"post","link":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/?p=1623","title":{"rendered":"\u6570\u5b66II_2Q2H_1"},"content":{"rendered":"\n\n\n\n
\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\nNext<\/span><\/a><\/td>\n<\/tr>\n
\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u518d\u751f\u30ea\u30b9\u30c8<\/span><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n
\u30c6\u30ad\u30b9\u30c8<\/span><\/td>\n\u6f14\u7fd2<\/span><\/td>\n\u6f14\u7fd2\u89e3\u7b54<\/span><\/td>\n\u8ab2\u984c<\/span><\/td>\n\u89e3\u8aac<\/span><\/td>\n<\/tr>\n
2Q2H_1<\/span><\/a><\/td>\n2Q2H_E1<\/span><\/a><\/td>\n2Q2H_ES1<\/span><\/a><\/td>\n2Q2H_K1<\/span><\/a><\/td>\n2Q2H_V1<\/span><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
<\/span> $a^\u2192+b^\u2192=?$\u3001$a^\u2192-b^\u2192=?$\u3001$ca^\u2192=?$\u3001 $|a^\u2192|=?$<\/div>
$\\vec{a}+\\vec{b}=$(\u77e2\u5370\u3092\u7e4b\u3044\u3067\u3001\u59cb\u70b9\u3068\u7d42\u70b9\u3092\u7d50\u3076)
\n$\\vec{a}-\\vec{b}=$($\\vec{a}$\u3068$\\vec{b}$\u306e\u9006\u30d9\u30af\u30c8\u30eb$-\\vec{b}$\u3092\u305f\u3059)
\n$c\\vec{a}=$($c>0$\u306e\u6642\u306f\u3001$c$\u500d\u3059\u308b\u3001$c<0$\u306e\u6642\u306f\u3001\u9006\u5411\u304d\u306b$|c|$\u500d\u3059\u308b)
\n$|\\vec{a}|=$(\u77e2\u5370\u306e\u9577\u3055)<\/p>\n

\"\"<\/div><\/div>

<\/span>Targets<\/div>
1. \u30d9\u30af\u30c8\u30eb $\\vec{a},\\vec{b}$\u3092\u4e0e\u3048\u3066\u3001
\n$\\quad$\u30d9\u30af\u30c8\u30eb\u306e\u7dda\u5f62\u548c\u3000$\\vec{c}=\\alpha\\vec{a}+\\beta\\vec{b}$<\/span> \u3092\u4f5c\u56f3\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b
\n$\\quad$\u307e\u305f\u3001\u30d9\u30af\u30c8\u30eb\u306e\u5927\u304d\u3055 $\\left|\\vec{c}\\right|$<\/span>\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b
\n2. \u6b63\u516d\u89d2\u5f62\u30fb\u4e09\u89d2\u5f62\u307e\u305f\u306f\u7acb\u65b9\u4f53\u306e
\n$\\quad$\u5e73\u884c\u3067\u306a\u30442\u8fba\u306b\u5411\u304d\u3092\u4ed8\u3051\u305f\u30d9\u30af\u30c8\u30eb $\\vec{a},\\vec{b}$ <\/span>\u3092\u4e0e\u3048\u3066\u3001\u4efb\u610f\u306e\u9802\u70b9\u3092
\n$\\quad$\u7d50\u3093\u3067\u3067\u304d\u308b\u30d9\u30af\u30c8\u30eb $\\vec{c}$ \u3092 $\\vec{a},\\vec{b}$ \u3092\u7528\u3044\u3066\u8868\u3059<\/span>\u3053\u3068\u304c\u3067\u304d\u308b <\/div><\/div> <\/div>\n
\n\n\n\n\n
2Q2H_2<\/span><\/a><\/td>\n2Q2H_E2<\/span><\/a><\/td>\n2Q2H_ES2<\/span><\/a><\/td>\n2Q2H_K2<\/span><\/a><\/td>\n2Q2H_V2<\/span><\/a><\/td>\n<\/tr>\n
\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n2Q2H_pf2<\/span><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
<\/span>\u5185\u7a4d $a^\u2192$\u30fb$b^\u2192=?$\u3001\u7dda\u5206\u306e\u4ea4\u70b9$P$\u3068\u59cb\u70b9$O$\u3092\u7d50\u3076\u30d9\u30af\u30c8\u30eb$OP^\u2192=?$<\/div>
$\\vec{a}\\cdot\\vec{b}=\\left|\\vec{a}\\right|\\left|\\vec{b}\\right|{\\mathrm{cos}} \\theta \\quad$<\/span> ($\\theta$ \u306f\u30d9\u30af\u30c8\u30eb $\\vec{a}, \\vec{b}$ \u306e\u306a\u3059\u89d2)<\/p>\n

\u76f4\u7dda ${\\mathrm{AB}}$ \u4e0a\u306e\u70b9 ${\\mathrm{P}}$<\/p>\n

\"\"<\/p>\n

\u30d9\u30af\u30c8\u30eb $\\vec{a}, \\vec{b}$ \u304c\u5e73\u884c\u3067\u306a\u3044\u3068\u304d
\n$\\alpha_1\\vec{a}+\\beta_1\\vec{b}=\\alpha_2\\vec{a}+\\beta_2\\vec{b} \\; \\Rightarrow \\; \\alpha_1=\\alpha_2, \\; \\beta_1=\\beta_2$<\/p>\n

\uff08\u53c2\u8003\uff09\u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406<\/span><\/p>\n

\"\"<\/p>\n<\/div><\/div>

<\/span>Targets<\/div>
1. \u5404\u8fba\u306e\u9577\u3055\u304c $l$ \u306e\u7acb\u65b9\u4f53\u3092\u4e0e\u3048\u3066\u3001\u5404\u9802\u70b9\u3092\u7d50\u3093\u3067\u3067\u304d\u308b\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d<\/span>
\n$\\quad$\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b
\n2. \u4e09\u89d2\u5f62 $\\triangle {\\mathrm{OAB}}$ \u3068\u30d9\u30af\u30c8\u30eb $\\overrightarrow{\\mathrm{OA}}=\\vec{a},\\;\\overrightarrow{\\mathrm{OB}}=\\vec{b}$ \u304a\u3088\u30732\u8fba\u306e\u5185\u5206\u70b9 $\\mathrm{C}, \\mathrm{D}$
\n$\\quad$\u3092\u4e0e\u3048\u3066\u3001\u7dda\u5206${\\mathrm{AD}}$ \u3068 ${\\mathrm{BC}}$ \u306e\u4ea4\u70b9\u3092 $\\mathrm{P}$ \u3068\u3059\u308b\u3068\u304d\u3001
\n$\\quad$\u30d9\u30af\u30c8\u30eb$\\overrightarrow{\\mathrm{OP}}$ \u3092 $\\vec{a}, \\vec{b}$ \u3092\u7528\u3044\u3066\u3042\u3089\u308f\u3059<\/span>\u3053\u3068\u304c\u3067\u304d\u308b<\/div><\/div> <\/div>\n
\n\n\n\n\n
2Q2H_3<\/span><\/a><\/td>\n2Q2H_E3<\/span><\/a><\/td>\n2Q2H_ES3<\/span><\/a><\/td>\n2Q2H_K3<\/span><\/a><\/td>\n2Q2H_V3<\/span><\/a><\/td>\n<\/tr>\n
\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n2Q2H_pf3<\/span><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
<\/span> $a^\u2192, b^\u2192$\u3000\u306e\u6210\u5206\u8868\u793a\u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d \u3000$|a^\u2192|=?$\u3001$pa^\u2192+qb^\u2192=?$\u3001$a^\u2192$\u30fb$b^\u2192=?$ <\/div>
$\\vec{a}=\\begin{pmatrix}a_1 \\\\ a_2 \\end{pmatrix}$\u3001$\\vec{b}=\\begin{pmatrix}b_1 \\\\ b_2 \\end{pmatrix}$ \u306e\u3068\u304d $|\\vec{a}|=\\sqrt{a_1^2+a_2^2}$<\/span>\u3001$|\\vec{b}|=\\sqrt{b_1^2+b_2^2}$<\/span>
\n$p\\vec{a}+q\\vec{b}=\\begin{pmatrix}pa_1+qb_1 \\\\ pa_2+qb_2 \\end{pmatrix}$<\/span>\u3001$\\vec{a}\\cdot\\vec{b}=a_1b_1+a_2b_2$<\/span>\u3001$\\vec{a}\\cdot\\vec{a}=a_1^2+a_2^2=|\\vec{a}|^2$<\/span>
\n$\\vec{a}, \\vec{b}$ \u306e\u306a\u3059\u89d2\u3092 $\\theta$ \u3068\u3059\u308b\u3068\u3001$\\theta={\\mathrm{cos}}^{-1}\\dfrac{\\vec{a}\\cdot\\vec{b}}{\\left|\\vec{a}\\right|\\left|\\vec{b}\\right|}$<\/span><\/div><\/div>
<\/span>Targets<\/div>
1. \u5ea7\u6a19\u5e73\u9762\u4e0a\u306b\u30d9\u30af\u30c8\u30eb\u3092\u4e0e\u3048\u3066\u3001\u6210\u5206\u8868\u793a\u3068\u5927\u304d\u3055<\/span>\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b
\n2. \u30d9\u30af\u30c8\u30eb $\\vec{a}, \\vec{b}$ \u306e\u6210\u5206\u8868\u793a\u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\u6b21\u304c\u8a08\u7b97\u3067\u304d\u308b
\n$\\quad$\u7dda\u5f62\u548c $p\\vec{a}+q\\vec{b}=?$<\/span>\u3001 \u5927\u304d\u3055 $|\\vec{a}|=?$<\/span>\u3001 \u5185\u7a4d $\\vec{a}\\cdot\\vec{b}=?$<\/span>
\n3. $|\\vec{a}|$ \u3068 $\\left|\\vec{b}\\right|$ \u304c\u308f\u304b\u3063\u3066\u3044\u308b\u3068\u304d\u3001
\n$\\quad$$\\left| \\vec{a}\\pm \\vec{b} \\right| \\Rightarrow \\vec{a}\\cdot\\vec{b}=?$<\/span>\u3001$ \\vec{a}\\cdot\\vec{b}\u3000\\Rightarrow \\left|\\vec{a}\\pm \\vec{b} \\right|=?$<\/span> <\/div><\/div> <\/div>\n\n\n\n
\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\nNext<\/span><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"

\u00a0 \u00a0 \u00a0 \u00a0 Next \u00a0 \u00a0 \u00a0 \u00a0 \u518d\u751f\u30ea\u30b9\u30c8 \u30c6\u30ad\u30b9\u30c8 \u6f14\u7fd2 \u6f14\u7fd2\u89e3\u7b54 \u8ab2\u984c \u89e3\u8aac 2Q2H_1 2Q2H_E1 2Q2H_ES1 2Q2H_K1 2Q2H_V1 2Q2H_2 2Q2H_E2 2Q2H_ES2 […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[42,14,4,8,35],"tags":[],"class_list":["post-1623","post","type-post","status-publish","format-standard","hentry","category-si","category-top","category-math2","category-math2-2q","category-math2-2q2h-1"],"_links":{"self":[{"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=\/wp\/v2\/posts\/1623","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1623"}],"version-history":[{"count":139,"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=\/wp\/v2\/posts\/1623\/revisions"}],"predecessor-version":[{"id":2951,"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=\/wp\/v2\/posts\/1623\/revisions\/2951"}],"wp:attachment":[{"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1623"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1623"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1623"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}