{"id":17779,"date":"2021-06-10T16:17:39","date_gmt":"2021-06-10T10:47:39","guid":{"rendered":"https:\/\/learnsteer.sasnaka.org\/science\/?p=17779"},"modified":"2022-01-28T10:04:21","modified_gmt":"2022-01-28T04:34:21","slug":"__trashed-9","status":"publish","type":"post","link":"https:\/\/learnsteer.sasnaka.org\/science\/advanced-level-science\/__trashed-9\/","title":{"rendered":"01.04.00 – \u0db4\u0dd2\u0dc4\u0dd2\u0da7\u0dd4\u0db8\u0dca \u0daf\u0ddb\u0dc1\u0dd2\u0d9a \u0dc3\u0db8\u0dca\u0db6\u0db1\u0dca\u0db0 \u0d85\u0db1\u0dd4\u0db4\u0dcf\u0dad \u0db4\u0dca\u200d\u0dbb\u0db8\u0dda\u0dba\u0dba"},"content":{"rendered":"\r\n
\r\n
\u0db4\u0dcf\u0da9\u0db8\u0dda \u0dc3\u0da7\u0dc4\u0db1 Download \u0d9a\u0dbb\u0d9c\u0db1\u0dca\u0db1.<\/a><\/div>\r\n<\/div>\r\n\r\n\r\n\r\n

O \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba\u0dba \u0d85\u0db1\u0dd4\u0db6\u0daf\u0dca\u0db0\u0dba\u0dd9\u0db1\u0dca A \u0dc4\u0dcf B \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba \u0dc0\u0dbd \u0db4\u0dd2\u0dc4\u0dd2\u0da7\u0dd4\u0db8\u0dca \u0daf\u0ddb\u0dc1\u0dd2\u0d9a a<\/span> \u0dc4\u0dcf b<\/span>\u00a0\u0db1\u0db8\u0dca A, B \u0dba\u0dcf \u0d9a\u0dbb\u0db1 \u0dbb\u0dda\u0d9b\u0dcf\u0dc0 C \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba\u0dba \u0db8\u0d9c\u0dd2\u0db1\u0dca m:n = AC:CB \u00a0\u0d85\u0db1\u0dd4\u0db4\u0dcf\u0dad\u0dba\u0da7 \u0db6\u0dd9\u0daf\u0dba\u0dd2 \u0db1\u0db8\u0dca, O \u0dbd\u0d9a\u0dca\u0dc2\u0dba\u0dba\u0da7 \u0dc3\u0dcf\u0db4\u0dda\u0d9a\u0dca\u0dc2\u0dc0 C \u0dc4\u0dd2 \u0db4\u0dd2\u0dc4\u0dd2\u0da7\u0dd4\u0db8\u0dca \u0daf\u0ddb\u0dc1\u0dd2\u0d9a\u0dba \u0d85\u0db1\u0dd4\u0db4\u0dcf\u0dad \u0db4\u0dca\u200d\u0dbb\u0db8\u0dda\u0dba\u0dba \u0da7 \u0d85\u0db1\u0dd4\u0dc0 \u0db4\u0dc4\u0dad \u0db4\u0dbb\u0dd2\u0daf\u0dd2 \u0dbd\u0db6\u0dcf \u0d9c\u0dad \u0dc4\u0dd0\u0d9a.<\/p>\r\n\r\n\r\n\r\n

{\\small\\overrightarrow {OA}}<\/span> \\small{\\overrightarrow {OA}}<\/span><\/p>\r\n\r\n\r\n\r\n

01. \u0d85\u0db7\u0dca\u200d\u0dba\u0db1\u0dca\u0dad\u0dbb\u0dc0 \u0db6\u0dd9\u0daf\u0dd9\u0db1 \u0d85\u0dc0\u0dc3\u0dca\u0dae\u0dcf\u0dc0.<\/span><\/h3>\r\n\r\n\r\n\r\n

\u0d85\u0db1\u0dd4\u0db4\u0dcf\u0dad \u0db4\u0dca\u200d\u0dbb\u0db8\u0dda\u0dba\u0dba \u0da7 \u0d85\u0db1\u0dd4\u0dc0,<\/p>\r\n\r\n\r\n\r\n

AC : CB = m : n <\/em>\u0db1\u0db8\u0dca,<\/p>\r\n\r\n\r\n\r\n\\overrightarrow{OC}\\;=\\;\\frac{m\\underline b+n\\underline a}{m+n}<\/span>\r\n\r\n\r\n\r\n

\u00a0<\/div>\r\n\r\n\r\n\r\n

\u0dc3\u0dcf\u0db0\u0db1\u0dba:\u00a0<\/p>\r\n\r\n\r\n\r\n\\begin{array}{rcl}\\overrightarrow{OC}\\;&=&\\overrightarrow{OA}+\\overrightarrow{AC}\\\\&&\\\\&=&\\underline{a\\;}+\\frac m{m+n}\\overrightarrow{AB}\\\\&&\\\\&=&\\underline{a\\;}+\\frac m{m+n}\\left(\\overrightarrow{AO}+\\overrightarrow{OB}\\right)\\\\&&\\\\&=&\\underline{a\\;}+\\frac m{m+n}\\left(-\\underline{a\\;}+\\underline b\\right)\\\\&&\\\\&=&\\frac{\\underline{a\\;}\\left(m+n\\right)-m\\underline{a\\;}+m\\underline b}{m+n}\\\\&&\\\\&=&\\frac{m\\underline b+n\\underline{a\\;}}{m+n}\\\\&&\\end{array}<\/span>\r\n\r\n\r\n\r\n

\u00a0<\/div>\r\n\r\n\r\n\r\n

\u0daf\u0ddb\u0dc1\u0dd2\u0d9a \u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab \u0db1\u0dd2\u0dba\u0db8\u0dba\u0da7 \u0d85\u0db1\u0dd4\u0dc0\u00a0<\/p>\r\n\r\n\r\n\r\n

02.\u0db6\u0dcf\u0dc4\u0dd2\u0dbb\u0dc0 \u0db6\u0dd9\u0daf\u0dd9\u0db1 \u0d85\u0dc0\u0dc3\u0dca\u0dae\u0dcf\u0dc0.<\/span><\/h3>\r\n\r\n\r\n\r\n

\u0d85\u0db1\u0dd4\u0db4\u0dcf\u0dad \u0db4\u0dca\u200d\u0dbb\u0db8\u0dda\u0dba\u0dba \u0da7 \u0d85\u0db1\u0dd4\u0dc0,<\/p>\r\n\r\n\r\n\r\n

AC : CB = m : n<\/em> \u0db1\u0db8\u0dca ,<\/p>\r\n\r\n\r\n\r\n\\overrightarrow{oc}\\;=\\;\\frac{m\\underline b+\\left(-n\\right)\\underline a}{m\\;+\\left(-n\\right)}<\/span>\r\n\r\n\r\n\r\n

\u00a0<\/div>\r\n\r\n\r\n\r\n\\overrightarrow{oc}\\;=\\;\\frac{m\\underline b-n\\underline a}{m\\;-n}<\/span>\r\n\r\n\r\n\r\n
\u00a0<\/div>\r\n\r\n\r\n\r\n

\u0dc3\u0dcf\u0db0\u0db1\u0dba:<\/p>\r\n\r\n\r\n\r\n

\u0daf\u0ddb\u0dc1\u0dd2\u0d9a \u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab \u0db1\u0dd2\u0dba\u0db8\u0dba\u0da7 \u0d85\u0db1\u0dd4\u0dc0,<\/p>\r\n\r\n\r\n\r\n

\\begin{array}{rcl}\\underline b\\;&=&\\frac{\\left(m-n\\right)\\underline c+n\\underline a}{\\left(m-n\\right)+n}\\\\&&\\\\m\\underline b\\;&=&\\;\\left(m-n\\right)\\underline c\\;+n\\underline a\\\\&&\\\\\\frac{m\\underline b-n\\underline a}{m-n}&=&\\underline c\\\\&&\\\\\\overrightarrow{OC}\\;&=&\\frac{m\\underline b-n\\underline a}{m-n}\\\\&&\\end{array}<\/span>\u00a0<\/p>\r\n\r\n\r\n\r\n

\u0d85\u0db1\u0dd4\u0db4\u0dcf\u0dad \u0db4\u0dca\u200d\u0dbb\u0db8\u0dda\u0dba\u0dba \u0dc0\u0dd2\u0db7\u0dda\u0daf\u0db1 \u0d86\u0d9a\u0dcf\u0dbb\u0dba.<\/span><\/h3>\r\n\r\n\r\n\r\n\\underline a\\;=\\;\\overrightarrow{OA\\;}=x_1\\;\\underline i\\;+\\;y_1\\;\\underline j<\/span>\r\n\r\n\r\n\r\n
\u00a0<\/div>\r\n\r\n\r\n\r\n\\underline b\\;=\\;\\overrightarrow{OB\\;}=x_2\\;\\underline i\\;+\\;y_2\\;\\underline j<\/span>\r\n\r\n\r\n\r\n
\u00a0<\/div>\r\n\r\n\r\n\r\n\\underline p\\;=\\;\\overrightarrow{OP\\;}=x\\;\\underline i\\;+\\;y\\;\\underline j<\/span>\r\n\r\n\r\n\r\n
\u00a0<\/div>\r\n\r\n\r\n\r\n

\u0db4\u0dca\u200d\u0dbb\u0db8\u0dda\u0dba\u0dba \u0d85\u0db1\u0dd4\u0dc0,<\/p>\r\n\r\n\r\n\r\n\\begin{array}{rcl}\\underline p&=&\\frac{\\left(n\\underline a+m\\underline b\\right)}{\\left(n+m\\right)}\\\\&&\\\\x\\;\\underline i+y\\;\\underline j\\;&=&\\frac{\\left[n\\left(x_1\\;\\underline i+y_2\\;\\underline j\\right)+m\\left(x_2\\;\\underline i+y_2\\;\\underline j\\right)\\right]}{\\left(n+m\\right)}\\\\&&\\\\&=&\\frac{\\left(nx_1+mx_2\\right)}{\\left(n+m\\right)}\\;\\underline i\\;+\\frac{\\left(ny_1+my_2\\right)}{\\left(n+m\\right)}\\;\\underline j\\;\\\\&&\\\\x\\;&=&\\;\\frac{\\left(nx_1+mx_2\\right)}{\\left(n+m\\right)}\\\\&&\\\\y\\;&=&\\;\\frac{\\left(ny_1+my_2\\right)}{\\left(n+m\\right)}\\\\&&\\\\p&\\equiv&\\left[\\;\\frac{\\left(nx_1+mx_2\\right)}{\\left(n+m\\right)},\\;\\frac{\\left(ny_1+my_2\\right)}{\\left(n+m\\right)}\\right]\\\\&&\\end{array}<\/span>\r\n\r\n\r\n\r\n

\u0dc0\u0dd0\u0daf\u0d9c\u0dad\u0dca<\/span><\/p>\r\n\r\n\r\n\r\n

    \r\n
  • \u0db8\u0dd9\u0db8 \u0db4\u0dca\u200d\u0dbb\u0db8\u0dda\u0dba\u0dba \u0dc0\u0dd2\u0dc2\u0dba \u0db1\u0dd2\u0dbb\u0dca\u0daf\u0dda\u0dc1\u0dba\u0da7 \u0d87\u0dad\u0dd4\u0dbd\u0dad\u0dca \u0db1\u0dd0\u0dad. \u0d91\u0db6\u0dd0\u0dc0\u0dd2\u0db1\u0dca \u0db4\u0dca\u200d\u0dbb\u0db8\u0dda\u0dba\u0dba \u0d8d\u0da2\u0dd4\u0dc0 \u0db7\u0dcf\u0dc0\u0dd2\u0dad\u0dba\u0dd9\u0db1\u0dca \u0d9c\u0dd0\u0da7\u0dbd\u0dd4 \u0dc0\u0dd2\u0dc3\u0daf\u0dd3\u0db8 \u0db1\u0ddc\u0d9a\u0dbd \u0dba\u0dd4\u0dad\u0dd4\u0dba.<\/li>\r\n
  • \u0db8\u0dd9\u0db8\u00a0 \u0db4\u0dca\u200d\u0dbb\u0db8\u0dda\u0dba\u0dba \u0db7\u0dcf\u0dc0\u0dd2\u0dad \u0dc0\u0db1 \u0d9c\u0dd0\u0da7\u0dbd\u0dd4 \u0dc0\u0dd2\u0db7\u0dcf\u0d9c\u0dba\u0da7 \u0db1\u0dd2\u0dad\u0dbb\u0db8 \u0d85\u0dc3\u0db1 \u0d85\u0dad\u0dbb \u0d92\u0dc0\u0dcf \u0dc3\u0dcf\u0db0\u0db1\u0dba \u0d9a\u0dbb\u0db1\u0dca\u0db1\u0dda, \u0db4\u0dca\u200d\u0dbb\u0db8\u0dda\u0dba\u0dba \u0dc3\u0dcf\u0db0\u0db1\u0dba \u0d9a\u0dbb\u0db1 \u0db8\u0dd6\u0dbd\u0db0\u0dbb\u0dca\u0db8 \u0db7\u0dcf\u0dc0\u0dd2\u0dad\u0dba\u0dd9\u0db1\u0dd2.<\/li>\r\n
  • \u0db8\u0dd9\u0db8 \u0db4\u0dca\u200d\u0dbb\u0db8\u0dda\u0dba\u0dba \u0db8 \u0d9b\u0dab\u0dca\u0da9\u0dcf\u0d82\u0d9a \u0da2\u0dca\u200d\u0dba\u0db8\u0dd2\u0dad\u0dd2\u0dba\u0dda\u0daf\u0dd3 \u0daf\u0dd3 \u0dc4\u0dcf \u0dc3\u0d82\u0d9a\u0dd3\u0dbb\u0dca\u0dab \u0dc3\u0d82\u0d9b\u0dca\u200d\u0dba\u0dcf \u0db4\u0dcf\u0da9\u0db8\u0dca \u0dc0\u0dbd \u0db1\u0dd0\u0dc0\u0dad \u0d89\u0d9c\u0dd9\u0db1\u0dd4\u0db8 \u0dbd\u0db6\u0dba\u0dd2.<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n

    \u0db4\u0dca\u200d\u0dbb\u0db8\u0dda\u0dba\u0dba\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\r\n\r\n\r\n\r\n

    \u00a0a<\/span><\/em> \u0dc4\u0dcf b<\/em><\/span> \u00a0\u0dba\u0db1\u0dd4 \u0d85\u0db7\u0dd2\u0dc1\u0dd6\u0db1\u0dca\u200d\u0dba \u0db1\u0ddc\u0dc0\u0db1 \u0dc4\u0dcf \u0dc3\u0db8\u0dcf\u0db1\u0dca\u0dad\u0dbb \u0db1\u0ddc\u0dc0\u0db1 \u0daf\u0ddb\u0dc1\u0dd2\u0d9a \u0daf\u0dd9\u0d9a\u0d9a\u0dca \u0db1\u0db8\u0dca \u0dc4\u0dcf \u03b1a<\/span><\/em> \u00a0+ \u03b2b<\/span><\/em> \u00a0= 0 \u0db8 \u0db1\u0db8\u0dca \u0db4\u0db8\u0dab\u0d9a\u0dca<\/p>\r\n\r\n\r\n\r\n

    \u03b1<\/em> = 0 \u0dc4\u0dcf \u03b2<\/em> = 0 \u0dc0\u0dda.<\/p>\r\n\r\n\r\n\r\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u0dc3\u0dcf\u0db0\u0db1\u0dba:<\/p>\r\n\r\n\r\n\r\n

    \u00a0a<\/span><\/em> \u0dc4\u0dcf b<\/span><\/em> \u00a0\u0daf\u0ddb\u0dc1\u0dd2\u0d9a \u0d85\u0dc3\u0db8\u0dcf\u0db1\u0dca\u0dad\u0dbb \u0db6\u0dd0\u0dc0\u0dd2\u0db1\u0dca,<\/p>\r\n\r\n\r\n\r\n

    a<\/span><\/em> \u2260 b<\/span><\/em> \u0dc4\u0dcf a \u2260 (-b<\/span><\/em>)<\/p>\r\n\r\n\r\n\r\n

    \u0dad\u0dc0\u0daf,<\/p>\r\n\r\n\r\n\r\n

    a<\/em><\/span> \u2260 0 \u0dc4\u0dcf b<\/span><\/em> \u2260 0 \u0db6\u0dc0 \u0daf\u0dd3 \u0d87\u0dad.<\/p>\r\n\r\n\r\n\r\n

    \u0d91\u0dc0\u0dd2\u0da7,<\/p>\r\n\r\n\r\n\r\n

    \u03b1a<\/span> <\/em>+ \u03b2b<\/span><\/em> =0 \u0dc0\u0dd3\u0db8\u0da7<\/p>\r\n\r\n\r\n\r\n

    \u03b1a<\/span> <\/em>= 0 \u0dc4\u0dcf \u03b2b<\/span><\/em> = 0 \u0dc0\u0dd2\u0dba \u0dba\u0dd4\u0dad\u0dd4\u0dba.<\/p>\r\n\r\n\r\n\r\n

    \u03b1<\/em> = 0 \u0dc4\u0dcf \u03b2<\/em> = 0 \u0dc0\u0dda. \u00a0<\/p>\r\n\r\n\r\n\r\n

    \u0d8b\u0daf\u0dcf:- a<\/span><\/em>\u00a0\u0dc4\u0dcf b<\/span><\/em> \u2260 0 \u0dc4\u0dcf \u0dc3\u0db8\u0dcf\u0db1\u0dca\u0dad\u0dbb \u0daf \u0db1\u0ddc\u0dc0\u0db1 \u0daf\u0ddb\u0dc1\u0dd2\u0d9a \u0daf\u0dd9\u0d9a\u0d9a\u0dca \u0dc0\u0db1 \u0d85\u0dad\u0dbb (2\u03bb + 3\u03bc \u2013 10) a<\/span><\/em> \u00a0+\u00a0\u00a0 (\u03bb \u2013 \u03bc \u2013 5) b<\/em><\/span> \u00a0= 0 \u0dbd\u0dd9\u0dc3 \u0db4\u0dca\u200d\u0dbb\u0d9a\u0dcf\u0dc1\u0db1\u0dba\u0d9a\u0dca \u0daf\u0dd3 \u0d87\u0dad. \u03bb \u0dc4\u0dcf \u03bc \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/p>\r\n\r\n\r\n\r\n

    \u00a0(2\u03bb + 3\u03bc \u2013 10) a<\/span><\/em> \u00a0+\u00a0\u00a0 (\u03bb \u2013 \u03bc \u2013 5) b<\/span><\/em> \u00a0= 0<\/p>\r\n\r\n\r\n\r\n

    a<\/span><\/em> \u2260 0 , b<\/span><\/em> \u2260 0 \u0dc4\u0dcf a<\/em><\/span> \u0dc4\u0dcf b <\/em><\/span>\u0daf\u0ddb\u0dc1\u0dd2\u0d9a \u0dc3\u0db8\u0dcf\u0db1\u0dca\u0dad\u0dbb \u0db1\u0ddc\u0dc0\u0db1 \u0db1\u0dd2\u0dc3\u0dcf,<\/p>\r\n\r\n\r\n\r\n

    (2\u03bb + 3\u03bc – 10) = 0 ————–\u00a0(1)<\/p>\r\n\r\n\r\n\r\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0(\u03bb \u2013 \u03bc – 5) = 0—————– \u00a0(2)<\/p>\r\n\r\n\r\n\r\n

    (2)\u0db1\u0dca,<\/p>\r\n\r\n\r\n\r\n

    \u03bb \u2013 \u03bc \u2013 5 = 0<\/p>\r\n\r\n\r\n\r\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u03bb = \u03bc + 5 ————–(3)\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\r\n\r\n\r\n\r\n

    (3)\u0db1\u0dca (1)\u0da7 \u0d86\u0daf\u0dda\u0dc1\u0dba,<\/p>\r\n\r\n\r\n\r\n

    2(\u03bc + 5) + 3\u03bc \u2013 10 = 0<\/p>\r\n\r\n\r\n\r\n

    \u00a02\u03bc + 10 + 3\u03bc \u2013 10 = 0<\/p>\r\n\r\n\r\n\r\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a05\u03bc = 0<\/p>\r\n\r\n\r\n\r\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u03bc = 0<\/p>\r\n\r\n\r\n\r\n

    \u0d91\u0dc0\u0dd2\u0da7 (3)\u0db1\u0dca,<\/p>\r\n\r\n\r\n\r\n

    \u03bb = 0 + 5<\/p>\r\n\r\n\r\n\r\n

    \u03bb = 5<\/p>\r\n\r\n\r\n\r\n

    \u0d8b\u0daf\u0dcf:- OACB \u0dc3\u0db8\u0dcf\u0db1\u0dca\u0dad\u0dbb\u0dcf\u0dc3\u0dca\u200d\u0dbb\u0dba\u0d9a\u0dd2. AC \u0db4\u0dcf\u0daf\u0dba\u0dda \u0db8\u0db0\u0dca\u200d\u0dba \u0dbd\u0d9a\u0dca\u0dc2\u0dba\u0dba D \u0daf AB \u0dc0\u0dd2\u0d9a\u0dbb\u0dca\u0dab\u0dba \u0db8\u0d9c\u0dd2\u0db1\u0dca OD \u0dbb\u0dda\u0d9b\u0dcf\u0dc0 2:1 \u0d85\u0db1\u0dd4\u0db4\u0dcf\u0dad\u0dba\u0dd9\u0db1\u0dca E \u0dc4\u0dd2\u0daf\u0dd3 \u0da1\u0dda\u0daf\u0db1\u0dba \u0dc0\u0dda. \\overrightarrow{OA}<\/span> = a<\/span><\/em> \u00a0\u0daf \\overrightarrow{OB}<\/span>\u00a0= b<\/em><\/span> \u0daf \u0db1\u0db8\u0dca \\overrightarrow{OD}<\/span>\u00a0\u0dc3\u0ddc\u0dba\u0dcf \\overrightarrow{AE}<\/span>\u00a0= \\overrightarrow{AB}<\/span> \/3 \u0db6\u0dc0 \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1.<\/p>\r\n\r\n\r\n\r\n

    \u00a0\\overrightarrow{OA}<\/span> = a<\/span><\/em><\/p>\r\n\r\n\r\n\r\n

    \u00a0\\overrightarrow{OB}<\/span> = b<\/span><\/em><\/p>\r\n\r\n\r\n\r\n

    \\overrightarrow{OD}<\/span> = \\overrightarrow{OA}<\/span> + \\overrightarrow{AD}<\/span><\/p>\r\n\r\n\r\n\r\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 = a<\/span><\/em>\u00a0+ \u00bd \\overrightarrow{AC}<\/span> \u00a0\u00a0 ;\u00a0\u00a0 (\u00bd AC = AD)<\/p>\r\n\r\n\r\n\r\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (AC \/\/ AD)<\/p>\r\n\r\n\r\n\r\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 = \u00a0a<\/span><\/em> + \u00bd \\overrightarrow{OB}<\/span> \u00a0\u00a0\u00a0 ;\u00a0\u00a0 (AC = OB)<\/p>\r\n\r\n\r\n\r\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (AC \/\/ OB)<\/p>\r\n\r\n\r\n\r\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 = \u00a0a<\/span><\/em> + \u00bd b<\/span><\/em><\/p>\r\n\r\n\r\n\r\n

    \u0db4\u0dc5\u0db8\u0dd4 \u0d9a\u0dca\u200d\u0dbb\u0db8\u0dba:<\/p>\r\n\r\n\r\n\r\n

    \\overrightarrow{AB}<\/span> = \\overrightarrow{AO}<\/span> + \\overrightarrow{OB}<\/span><\/p>\r\n\r\n\r\n\r\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 = \u00a0\\overrightarrow{OB}<\/span> – \\overrightarrow{OA}<\/span><\/p>\r\n\r\n\r\n\r\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 = \u00a0b<\/span> <\/em>– a<\/span><\/em><\/p>\r\n\r\n\r\n\r\n

    \u00a0\\overrightarrow{AE}<\/span> = \\overrightarrow{AO}<\/span> + \\overrightarrow{OE}<\/span><\/p>\r\n\r\n\r\n\r\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 = \u00a0\\overrightarrow{AO}<\/span> + 2\/3<\/em> \\overrightarrow{OD}<\/span>\u00a0\u00a0\u00a0 ;\u00a0\u00a0 (2\/3<\/em> OD = OE)<\/p>\r\n\r\n\r\n\r\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0(OD \/\/ OE)<\/p>\r\n\r\n\r\n\r\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 = 2\/3 \\overrightarrow{OD}<\/span>\u00a0\u2013 \\overrightarrow{OA}<\/span><\/p>\r\n\r\n\r\n\r\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 = 2\/3 ( a\u00a0+\u00bd b ) \u2013 a<\/span><\/em><\/p>\r\n\r\n\r\n\r\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 = 1\/3 ( b<\/span><\/em>\u00a0\u2013 a<\/em><\/span> )<\/p>\r\n\r\n\r\n\r\n

    \u00a0\\overrightarrow{AE}<\/span> = 1\/3 \\overrightarrow{AB}<\/span><\/p>\r\n\r\n\r\n\r\n

    \u0daf\u0dd9\u0dc0\u0db1 \u0d9a\u0dca\u200d\u0dbb\u0db8\u0dba: \u0d85\u0db1\u0dd4\u0db4\u0dcf\u0dad\u0dba \u0db8\u0d9c\u0dd2\u0db1\u0dca,\u00a0<\/em><\/p>\r\n\r\n\r\n\r\n

    \u00a0\\overrightarrow{OE}<\/span>= 2\/3 \\overrightarrow{OD}<\/span> \u00a0\u00a0\u00a0\u00a0<\/p>\r\n\r\n\r\n\r\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 = 2\/3 ( a<\/span><\/em>\u00a0+\u00bd b<\/span><\/em> ) —————-(1)<\/p>\r\n\r\n\r\n\r\n

    \u0dad\u0dc0\u0daf,\u00a0\u00a0<\/p>\r\n\r\n\r\n\r\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \\overrightarrow{OE}<\/span>= (\u03bb \u00d7 a<\/em><\/span>\u00a0+ 1 \u00d7 b<\/span> )\/ (\u03bb + 1)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (\u0d85\u0db7\u0dca\u200d\u0dba\u0db1\u0dca\u0dad\u0dbb \u0db6\u0dd9\u0daf\u0dd3\u0db8 \u0dc3\u0dbd\u0d9a\u0dcf)<\/p>\r\n\r\n\r\n\r\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 = (\u03bb a<\/span><\/em> + b<\/em><\/span> )\/ (\u03bb + 1)————-(2)<\/p>\r\n\r\n\r\n\r\n

    (1) = (2)\u0db1\u0dca,<\/p>\r\n\r\n\r\n\r\n

    \u00a02\/3 ( a<\/span><\/em>\u00a0+\u00bd b<\/span><\/em> ) = (\u03bb a<\/span><\/em>\u00a0+ b<\/span><\/em> )\/ (\u03bb + 1)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\r\n\r\n\r\n\r\n

    2\/3 a<\/span><\/em>\u00a0+ 1\/3 b<\/span><\/em>\u00a0= (\u03bb\/(\u03bb + 1)) \u00a0+ (1\/(\u03bb + 1)) \u00a0<\/p>\r\n\r\n\r\n\r\n

    \u00a0\u0dc4\u0dd2 \u0dc3\u0d82\u0d9c\u0dd4\u0dab\u0d9a \u0dc3\u0db8\u0dcf\u0db1 \u0d9a\u0dd2\u0dbb\u0dd3\u0db8\u0dd9\u0db1\u0dca,<\/p>\r\n\r\n\r\n\r\n

    1\/3 = 1\/(\u03bb + 1)<\/p>\r\n\r\n\r\n\r\n

    \u03bb + 1 = 3<\/p>\r\n\r\n\r\n\r\n

    \u00a0\u00a0\u00a0\u00a0\u00a0 \u03bb = 2\u00a0<\/p>\r\n\r\n\r\n\r\n

    \u0d91\u0db8\u0db1\u0dd2\u0dc3\u0dcf \u0db8\u0dd9\u0dc4\u0dd2,<\/p>\r\n\r\n\r\n\r\n

    AE : EB = 1:2<\/p>\r\n\r\n\r\n\r\n

    AE : AB = 1:3<\/p>\r\n\r\n\r\n\r\n

    \u00a0<\/div>\r\n\r\n\r\n\r\n

    \\overrightarrow{OA}<\/span> =1\/3<\/p>\r\n\r\n\r\n\r\n

    \\overrightarrow{AB}<\/span> ;\u00a0\u00a0\u00a0 (AE = 1\/3 AB)<\/p>\r\n\r\n\r\n\r\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0(AE \/\/ AB)<\/p>\r\n\r\n\r\n\r\n