{"id":13304,"date":"2021-04-06T02:35:31","date_gmt":"2021-04-05T21:05:31","guid":{"rendered":"https:\/\/learnsteer.sasnaka.org\/science\/?p=13304"},"modified":"2022-01-24T22:30:41","modified_gmt":"2022-01-24T17:00:41","slug":"03-02-03","status":"publish","type":"post","link":"https:\/\/learnsteer.sasnaka.org\/science\/advanced-level-science\/combined-mathematics\/03-02-03\/","title":{"rendered":"03.02.03 &#8211; \u0da1\u0dda\u0daf\u0db1\u0dba \u0dc0\u0db1 \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf \u0daf\u0dd9\u0d9a\u0d9a\u0dca \u0d85\u0dad\u0dbb \u0d9a\u0ddd\u0dab\u0dba"},"content":{"rendered":"\r\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-block-buttons-is-layout-flex\">\r\n<div class=\"wp-block-button is-style-shadow\"><a class=\"wp-block-button__link\" style=\"border-radius: 15px\" href=\"https:\/\/drive.google.com\/uc?id=1V7RWunm1xD6vLeD8lCn1S2Xo2hhlaiEz&amp;export=download\" target=\"_blank\" rel=\"noreferrer noopener\">\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<ul class=\"wp-block-list\">\r\n<li>\u0d91\u0d9a\u0d9a\u0dca \u0d85\u0db1\u0dd9\u0d9a\u0da7 \u0dc3\u0db8\u0dcf\u0db1\u0dca\u0dad\u0dbb \u0db1\u0ddc\u0dc0\u0dd6 \u0daf,\u0d91\u0d9a\u0d9a\u0dca \u0d85\u0db1\u0dd9\u0d9a\u0da7 \u0dbd\u0db8\u0dca\u0db6 \u0db1\u0ddc\u0dc0\u0dd6 \u0daf,\u0dbb\u0dda\u0d9b\u0dcf \u0daf\u0dd9\u0d9a\u0d9a \u0d85\u0db1\u0dd4\u0d9a\u0dca\u200d\u0dbb\u0db8\u0dab m<sub>1 <\/sub>\u0dc4\u0dcf m<sub>2 <\/sub>\u0dba\u0dd0\u0dba\u0dd2 \u0d9c\u0db1\u0dd2\u0db8\u0dd4.\u0db8\u0dda\u0dc0\u0dcf \u0db4\u0dd2\u0dc5\u0dd2\u0dc0\u0dd9\u0dbd\u0dd2\u0db1\u0dca OX \u0dc4\u0dd2 \u0db0\u0db1 \u0daf\u0dd2\u0dc1\u0dcf\u0dc0 \u0dc3\u0db8\u0d9f <span class=\"wp-katex-eq\" data-display=\"false\">\\theta_1\\text{\u0dc4\u0dcf}\\theta_2<\/span> <sub>\u00a0<\/sub>\u0d9a\u0ddd\u0dab \u0dc3\u0dcf\u0daf\u0dba\u0dd2.<\/li>\r\n<\/ul>\r\n<p><img loading=\"lazy\" decoding=\"async\" width=\"2133\" height=\"2133\" class=\"alignnone wp-image-35104 size-full\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/04\/Pasted-into-03.02.03-\u0da1\u0dda\u0daf\u0db1\u0dba-\u0dc0\u0db1-\u0dc3\u0dbb\u0dbd-\u0dbb\u0dda\u0d9b\u0dcf-\u0daf\u0dd9\u0d9a\u0d9a\u0dca-\u0d85\u0dad\u0dbb-\u0d9a\u0ddd\u0dab\u0dba.png\" \/><\/p>\r\n\r\n\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">tan\\theta_1=m_1<\/span><span class=\"wp-katex-eq\" data-display=\"false\">\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;<\/span><span class=\"wp-katex-eq\" data-display=\"false\">tan\\theta_2=m_2<\/span><\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf \u0daf\u0dd9\u0d9a \u0d85\u0dad\u0dbb \u0d9a\u0ddd\u0dab\u0dba \u0d9a\u0dd4\u0db8\u0d9a\u0dca \u0dc0\u0dd4\u0dc0\u0dad\u0dca,\u00a0\u00a0<span class=\"wp-katex-eq\" data-display=\"false\">\u00a0\\alpha+\\theta_2=\\theta_1<\/span>\u00a0 \u0dc0\u0dda.<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\Rightarrow\\alpha=\\theta_1-\\theta_2<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">tan\\alpha=tan(\\theta_1-\\theta_2)<\/span><\/p>\r\n\r\n\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}tan\\alpha&amp;=&amp;tan(\\theta_1-\\theta_2)\\\\&amp;=&amp;\\frac{tan(\\theta_1)-tan(\\theta_2)}{1+tan(\\theta_1).tan(\\theta_2)}\\\\&amp;=&amp;\\frac{m_1-m_2}{1+m_1m_2}\\\\\\alpha&amp;=&amp;\\tan^{-1}\\left(\\frac{m_1-m_2}{1+m_1m_2}\\right)\\end{array}<\/span>\r\n\r\n\r\n\r\n<p>\u00a0<span class=\"wp-katex-eq\" data-display=\"false\">\\frac{m_1-m_2}{1+m_1m_2}&gt;0<\/span>\u0db1\u0db8\u0dca \u00a0\u0dc3\u0dd4\u0dc5\u0dd4 \u0d9a\u0ddd\u0dab\u0dba\u0d9a\u0dca \u0dc0\u0db1 \u0d85\u0dad\u0dbb \u0d91\u0db8 \u0d85\u0d9c\u0dba \u0dc3\u0dd8\u0dab \u0db1\u0db8\u0dca<span class=\"wp-katex-eq\" data-display=\"false\">\\theta<\/span> \u00a0\u0db8\u0dc4\u0dcf \u0d9a\u0ddd\u0dab\u0dba\u0d9a\u0dca \u0dc0\u0dda.<\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li><span class=\"has-inline-color has-vivid-red-color\">\u00a0<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\theta\\end{array}<\/span>\u0db8\u0d9c\u0dd2\u0db1\u0dca \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf \u0daf\u0dd9\u0d9a\u0d9a\u0dca \u0d85\u0dad\u0dbb \u0dc3\u0dd4\u0dc5\u0dd4 \u0d9a\u0ddd\u0dab\u0dba \u0daf\u0d9a\u0dca\u0dc0\u0dba\u0dd2 \u0db1\u0db8\u0dca,<\/span><\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"has-inline-color has-vivid-red-color\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}tan\\theta&amp;=&amp;\\left|\\frac{m_1-m_2}{1+m_1m_2}\\right|\\end{array}<\/span><\/span><\/p>\r\n\r\n\r\n\r\n<p>\u0d8b\u0daf\u0dcf : (1.) x + y = 0 \u0dc4\u0dcf 2x \u2013 y + 1 = 0 \u0dbb\u0dda\u0d9b\u0dcf \u0daf\u0dd9\u0d9a \u0d85\u0dad\u0dbb \u0d87\u0dad\u0dd2 \u0dc3\u0dd4\u0dc5\u0dd4 \u0d9a\u0ddd\u0dab\u0dba <sup>\ud835\udfb9<\/sup>\u2215 <sub>4 <\/sub>\u0da7 \u0dc0\u0dd0\u0da9\u0dd2 \u0db6\u0dc0 \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1.<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}x+y&amp;=&amp;0\\;\\;\\;\\;\\;\\;\\Rightarrow\\;\\;\\;\\;y=-x\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<p>x + y = 0 \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0dda \u0d85\u0db1\u0dd4\u0d9a\u0dca\u200d\u0dbb\u0db8\u0dab\u0dba = -1<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">2x-y+1=0\\;\\;\\;\\;\\Rightarrow\\;\\;\\;\\;y=2x+1<\/span><\/p>\r\n\r\n\r\n\r\n<p>2x \u2013 y + 1 = 0 \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0dda \u0d85\u0db1\u0dd4\u0d9a\u0dca\u200d\u0dbb\u0db8\u0dab\u0dba = 2<\/p>\r\n\r\n\r\n\r\n<p>\u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf \u0daf\u0dd9\u0d9a \u0d85\u0dad\u0dbb \u0dc3\u0dd4\u0dc5\u0dd4 \u0d9a\u0ddd\u0dab\u0dba <span class=\"wp-katex-eq\" data-display=\"false\">\\alpha<\/span>\u00a0\u0db1\u0db8\u0dca,<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\tan\\alpha&amp;=&amp;\\left|\\frac{2-(-1)}{1+2\\times(-1)}\\right|\\\\\\tan\\alpha&amp;=&amp;3&gt;1\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;\\Rightarrow&amp;\\tan\\alpha&gt;\\tan\\left(\\pi\/4\\right)\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\u200d\\alpha&amp;&gt;&amp;\\pi\/4\\;\\;\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u0daf\u0dd3 \u0d87\u0dad\u0dd2 \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf \u0daf\u0dd9\u0d9a \u0d85\u0dad\u0dbb \u0dc3\u0dd4\u0dc5\u0dd4 \u0d9a\u0ddd\u0dab\u0dba <span class=\"wp-katex-eq\" data-display=\"false\">\\pi\/4<\/span>\u00a0\u0da7 \u0dc0\u0da9\u0dcf \u0dc0\u0dd0\u0da9\u0dd2 \u0dc0\u0dda.<\/p>\r\n\r\n\r\n\r\n<p>\u0d8b\u0daf\u0dcf: (2)<span class=\"wp-katex-eq\" data-display=\"false\">y-y_0=m(x-x_0)<\/span>\u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0<span class=\"wp-katex-eq\" data-display=\"false\">y-y_0=m&#039;(x-x_0);m\\;\\neq\\;m&#039;<\/span> \u0dc3\u0db8\u0d9c 45<sup>0 <\/sup>\u0d9a \u0d9a\u0ddd\u0dab\u0dba\u0d9a\u0dca \u0dc3\u0dcf\u0daf\u0dba\u0dd2 \u0db1\u0db8\u0dca \u00a0<span class=\"wp-katex-eq\" data-display=\"false\">m=\\frac{1+m&#039;}{1-m&#039;}<\/span> \u0dc4\u0ddd <span class=\"wp-katex-eq\" data-display=\"false\">m=-\\frac{1-m&#039;}{1+m&#039;}<\/span>\u00a0\u0db6\u0dc0 \u0dc3\u0dcf\u0db0\u0db1\u0dba \u0d9a\u0dbb\u0db1\u0dca\u0db1.<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">y-y_0=m(x-x_0)\\Rightarrow y=mx+y_0-mx_0<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">y-y_0=m&#039;(x-x_0)\\Rightarrow y=m&#039;x+y_0-m&#039;x_0<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">tan\\alpha=mtan\\beta=m<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\theta+\\beta=\\alpha<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\Rightarrow\\theta=\\alpha-\\beta<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\tan\\theta&amp;=&amp;\\tan(\\alpha-\\beta)\\\\&amp;=&amp;\\frac{\\tan\\alpha-\\tan\\beta}{1+\\tan\\alpha\\tan\\beta\\;}\\\\&amp;=&amp;\\frac{m-m&#039;}{1+mm&#039;}\\end{array}<\/span><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" width=\"2133\" height=\"2133\" class=\"alignnone wp-image-35106 size-full\" src=\"https:\/\/learnsteer.sasnaka.org\/science\/wp-content\/uploads\/sites\/3\/2021\/04\/Pasted-into-03.02.03-\u0da1\u0dda\u0daf\u0db1\u0dba-\u0dc0\u0db1-\u0dc3\u0dbb\u0dbd-\u0dbb\u0dda\u0d9b\u0dcf-\u0daf\u0dd9\u0d9a\u0d9a\u0dca-\u0d85\u0dad\u0dbb-\u0d9a\u0ddd\u0dab\u0dba-1.png\" \/><\/p>\r\n\r\n\r\n\r\n\r\n\r\n<p><span class=\"wp-katex-eq\" data-display=\"false\">\\theta=45^0<\/span>\u0dc4\u0ddd <span class=\"wp-katex-eq\" data-display=\"false\">\u200d\\theta=135^0<\/span>\u0dc0\u0dda \u0d91\u0dc0\u0dd2\u0da7 <span class=\"wp-katex-eq\" data-display=\"false\">\\tan\\theta=\\pm1\\;<\/span>\u00a0\u0dc0\u0dda.<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\pm1=\\frac{m-m&#039;}{1+mm&#039;}<\/span><\/p>\r\n\r\n\r\n\r\n<p>+\u0dc3\u0dd0\u0dbd\u0d9a\u0dd3\u0db8\u0dd9\u0db1\u0dca,<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}1&amp;=&amp;\\frac{m-m&#039;}{1+mm&#039;}\\\\1+mm&#039;&amp;=&amp;m-m&#039;\\\\m(1-m&#039;)&amp;=&amp;1+m&#039;\\\\m&amp;=&amp;\\frac{1+m&#039;}{1-m&#039;}\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<p>-\u0dc3\u0dd0\u0dbd\u0d9a\u0dd3\u0db8\u0dd9\u0db1\u0dca,<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}-1&amp;=&amp;\\frac{m-m&#039;}{1+mm&#039;}\\\\-\\left(1+mm&#039;\\right)&amp;=&amp;m-m&#039;\\\\m(1+m&#039;)&amp;=&amp;m&#039;-1\\\\m&amp;=&amp;-\\left(\\frac{1-m&#039;}{1+m&#039;}\\right)\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<p><strong>\u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf \u0daf\u0dd9\u0d9a\u0d9a\u0dca \u0dc3\u0db8\u0dcf\u0db1\u0dca\u0dad\u0dbb\u0dc0\u0dd3\u0db8 \u0dc3\u0db3\u0dc4\u0dcf \u0d85\u0dc0\u0dc1\u0dca\u200d\u0dba\u0dad\u0dcf\u0dc0\u0dba \u0d85\u0db4\u0ddd\u0dc4\u0db1\u0dba<\/strong><\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u00a0<span class=\"wp-katex-eq\" data-display=\"false\">y=m_1x+c_1<\/span>\u00a0\u0dc4\u0dcf\u00a0 <span class=\"wp-katex-eq\" data-display=\"false\">y=m_2x+c_2<\/span>\u00a0\u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf \u0daf\u0dd9\u0d9a \u0d85\u0dad\u0dbb \u0d9a\u0ddd\u0dab\u0dba <span class=\"wp-katex-eq\" data-display=\"false\">\\theta\\;<\/span>\u00a0\u0dbd\u0dd9\u0dc3 \u0d9c\u0db1\u0dd2\u0db8\u0dd4.<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">tan\\theta=\\frac{m_1-m_2}{1+m_1m_2}<\/span><\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf \u0daf\u0dd9\u0d9a \u0d91\u0d9a\u0dd2\u0db1\u0dd9\u0d9a\u0da7 \u0dc3\u0db8\u0dcf\u0db1\u0dca\u0dad\u0dbb \u0dc0\u0db1 \u0dc0\u0dd2\u0da7 <span class=\"wp-katex-eq\" data-display=\"false\">\\theta=0<\/span>\u00a0\u0dc4\u0ddd <span class=\"wp-katex-eq\" data-display=\"false\">\\theta=\\pi<\/span>\u00a0\u0dc0\u0dda. \u0db8\u0dd9\u0dc0\u0dd2\u0da7 <span class=\"wp-katex-eq\" data-display=\"false\">\\tan\\theta=0<\/span> \u0dc0\u0dda.<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{l}\\Rightarrow\\;\\;\\;\\;\\;\\;\\frac{m_1-m_2}{1+m_1m_2}=0\\\\{\\Rightarrow\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;m_1=m_2}\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf \u0daf\u0dd9\u0d9a\u0d9a\u0dca \u0dc3\u0db8\u0dcf\u0db1\u0dca\u0dad\u0dbb \u0db1\u0db8\u0dca \u0dc3\u0dc4 \u0d91\u0db1\u0db8\u0dca \u0db4\u0db8\u0dab\u0d9a\u0dca \u0d92\u0dc0\u0dcf\u0dba\u0dda \u0d85\u0db1\u0dd4\u0d9a\u0dca\u200d\u0dbb\u0db8\u0dab \u0dc3\u0db8\u0dcf\u0db1 \u0dc0\u0dda.<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p>\u0d8b\u0daf\u0dcf :<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{l}3x-y-4=0\\end{array}<\/span> \u00a0\u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0da7 \u0dc3\u0db8\u0dcf\u0db1\u0dca\u0dad\u0dbb\u0dc0 (1, 2) \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba \u0dc4\u0dbb\u0dc4\u0dcf \u0dba\u0db1 \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0dda \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf \u0daf\u0dd9\u0d9a \u0dc3\u0db8\u0dcf\u0db1\u0dca\u0dad\u0dbb \u0dc0\u0dd2\u0da7 \u0d92\u0dc0\u0dcf\u0dba\u0dda \u0d85\u0db1\u0dd4\u0d9a\u0dca\u200d\u0dbb\u0db8\u0dab \u0dc3\u0db8\u0dcf\u0db1 \u0dc0\u0dda.<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p>\u00a0<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{l}\\therefore\\;\\end{array}<\/span>\u0db8\u0dd9\u0db8 \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0da7 \u0dc3\u0db8\u0dcf\u0db1\u0dca\u0dad\u0dbb (1, 2) \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba\u0dba \u0dc4\u0dbb\u0dc4\u0dcf \u0dba\u0db1 \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0dda \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba,<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{l}(y-2)=3(x-1)\\\\3x-y-1=0\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<p><strong>\u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf \u0daf\u0dd9\u0d9a\u0d9a\u0dca \u0dbd\u0db8\u0dca\u0db7\u0d9a\u0dc0\u0dd3\u0db8 \u0dc3\u0db3\u0dc4\u0dcf \u0d85\u0dc0\u0dc1\u0dca\u200d\u0dba\u0dad\u0dcf\u0dc0\u0dba \u0d85\u0db4\u0ddd\u0dc4\u0db1\u0dba<\/strong><\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li><span class=\"wp-katex-eq\" data-display=\"false\">y=m_1x+c_1<\/span>\u00a0\u0dc4\u0dcf\u00a0 <span class=\"wp-katex-eq\" data-display=\"false\">y=m_2x+c_2<\/span>\u00a0\u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf \u0daf\u0dd9\u0d9a \u0d85\u0dad\u0dbb \u0d9a\u0ddd\u0dab\u0dba <span class=\"wp-katex-eq\" data-display=\"false\">\\theta<\/span>\u00a0\u0dbd\u0dd9\u0dc3 \u0d9c\u0db1\u0dd2\u0db8\u0dd4.<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">tan\\theta=\\frac{m_1-m_2}{1+m_1m_2}<\/span><\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf \u0daf\u0dd9\u0d9a \u0d91\u0d9a\u0dd2\u0d9a\u0dd9\u0da7 \u0dbd\u0db8\u0dca\u0db7\u0d9a \u0dc0\u0db1 \u0dc0\u0dd2\u0da7 <span class=\"wp-katex-eq\" data-display=\"false\">\\theta=\\pi\/2<\/span>\u00a0\u0dc0\u0dda. \u0db8\u0dd9\u0dc0\u0dd2\u0da7 <span class=\"wp-katex-eq\" data-display=\"false\">\\tan\\theta<\/span>\u00a0\u0da7 \u0d85\u0dbb\u0dca\u0dae \u0db1\u0dd0\u0dad. \u0db8\u0dda \u0dc3\u0db3\u0dc4\u0dcf <span class=\"wp-katex-eq\" data-display=\"false\">1+m_1m_2=0<\/span>\u00a0\u0dc0\u0dd2\u0dba \u0dba\u0dd4\u0dad\u0dd4\u0dba\u0dd2.<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">1+m_1m_2=0\\;\\;\\;\\;\\;\\Rightarrow\\;\\;\\;\\;\\;m_1m_2=-1<\/span><\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf \u0daf\u0dd9\u0d9a\u0d9a\u0dca \u0d91\u0d9a\u0dd2\u0db1\u0dd9\u0d9a\u0da7 \u0dbd\u0db8\u0dca\u0db7\u0d9a \u0db1\u0db8\u0dca \u0dc3\u0dc4 \u0d91\u0db1\u0db8\u0dca \u0db4\u0db8\u0dab\u0d9a\u0dca \u0d92\u0dc0\u0dcf\u0dba\u0dda \u0d85\u0db1\u0dd4\u0d9a\u0dca\u200d\u0dbb\u0db8\u0dab \u0d9c\u0dd4\u0dab\u0dd2\u0dad\u0dba -1 \u0d9a\u0dca \u0dc0\u0dda.<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p>\u0d8b\u0daf\u0dcf : <span class=\"wp-katex-eq\" data-display=\"false\">2x-3y+1=0<\/span>\u00a0\u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0da7 \u0dbd\u0db8\u0dca\u0db7\u0d9a\u0dc0 (-3, -4) \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba\u0dba\u0dc4\u0dbb\u0dc4\u0dcf \u0dba\u0db1 \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0dda \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/p>\r\n\r\n\r\n\r\n<p>\u0daf\u0dd3 \u0d87\u0dad\u0dd2 \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0d9a\u0da7 \u0dbd\u0db8\u0dca\u0db7\u0d9a \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0d9a \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba,<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">3x+2y+k=0<\/span><\/p>\r\n\r\n\r\n\r\n<p>\u0db8\u0dd9\u0db8 \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0 (-3, -4) \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba\u0dba \u0dc4\u0dbb\u0dc4\u0dcf \u0dba\u0db1 \u0db6\u0dd0\u0dc0\u0dd2\u0db1\u0dca \u0d91\u0db8 \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba\u0dba\u0dda \u0d9b\u0dab\u0dca\u0da9\u0dcf\u0d82\u0d9a \u0db8\u0d9c\u0dd2\u0db1\u0dca \u0dad\u0dd8\u0db4\u0dca\u0dad \u0d9a\u0dbb\u0dba\u0dd2.<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{l}3(-3)+2(-4)+k=0\\\\\\Longrightarrow k=17\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u0d85\u0dc0\u0dc1\u0dca\u200d\u0dba \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0dda \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba,<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">3x+2y+17=0<\/span><\/p>\r\n\r\n\r\n\r\n<div class=\"wp-block-spacer\" style=\"height: 100px\" aria-hidden=\"true\">\u00a0<\/div>\r\n\r\n\r\n\r\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-block-buttons-is-layout-flex\">\r\n<div class=\"wp-block-button is-style-shadow td_btn_normal\"><a class=\"wp-block-button__link\" style=\"border-radius: 15px\" href=\"https:\/\/drive.google.com\/uc?id=1V7RWunm1xD6vLeD8lCn1S2Xo2hhlaiEz&amp;export=download\" target=\"_blank\" rel=\"noreferrer noopener\">\u0db4\u0dcf\u0da9\u0db8\u0dda \u0dc3\u0da7\u0dc4\u0db1 Download \u0d9a\u0dbb\u0d9c\u0db1\u0dca\u0db1.<\/a><\/div>\r\n<\/div>\r\n<div>\u00a0<\/div>\r\n<div>\u00a0<\/div>\r\n<div>\u00a0<\/div>\r\n<div class=\"wp-block-buttons is-content-justification-center\">\r\n<div><a class=\"wp-block-button__link\" style=\"border-radius: 15px\" href=\"https:\/\/drive.google.com\/drive\/folders\/1otlWj3tqtLlKXwTQeg1Fpf3aZMecmgUd?usp=sharing\" target=\"_blank\" rel=\"noreferrer noopener\">\u0dad\u0dc0\u0dad\u0dca \u0db4\u0dca\u200d\u0dbb\u0dc1\u0dca\u0db1 \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1.<\/a><\/div>\r\n<\/div>\r\n\r\n\r\n\r\n<div class=\"wp-block-spacer\" style=\"height: 100px\" aria-hidden=\"true\">\u00a0<\/div>\r\n\r\n\r\n\r\n<div class=\"wp-block-spacer\" style=\"height: 100px\" aria-hidden=\"true\">\u00a0<\/div>\r\n","protected":false},"excerpt":{"rendered":"<p>\u0d85\u0db1\u0dd4\u0d9a\u0dca\u200d\u0dbb\u0db8\u0dab \u0d87\u0dc3\u0dd4\u0dbb\u0dd9\u0db1\u0dca \u0daf\u0dd9\u0db1 \u0dbd\u0daf \u0dbb\u0dda\u0d9b\u0dcf \u0daf\u0dd9\u0d9a\u0d9a\u0dca \u0d85\u0dad\u0dbb \u0d9a\u0ddd\u0dab\u0dba \u0dc3\u0dd9\u0dc0\u0dd3\u0db8 \u0dc3\u0dc4 \u0dc3\u0dbb\u0dbd \u0dbb\u0dda\u0d9b\u0dcf \u0daf\u0dd9\u0d9a\u0d9a\u0dca \u0dc3\u0db8\u0dcf\u0db1\u0dca\u0dad\u0dbb \u0dc4\u0ddd \u0dbd\u0db8\u0dca\u0db6 \u0dc0\u0dd3\u0db8\u0da7 \u0d85\u0dc0\u0dc1\u0dca\u200d\u0dba\u0dad\u0dcf\u0dc0 \u0dc3\u0dd9\u0dc0\u0dd3\u0db8 \u0dc3\u0dd2\u0daf\u0dd4 \u0d9a\u0dbb\u0dba\u0dd2.<\/p>\n","protected":false},"author":75,"featured_media":16874,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"tdm_status":"","tdm_grid_status":"","footnotes":""},"categories":[3665,3634,42,3630,3629],"tags":[1023,4260,3808,3862,3886,4259,4265,4266,4258,4264,4241,4261,1020,4176,4152,3579,4252,1019,3792,3795,3873,4169,4262,4263,4255,3798,3802,4249,4244,3588,3874],"class_list":{"0":"post-13304","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-03-02-straight-line","8":"category-03-coordinate-geometry","9":"category-advanced-level-science","10":"category-pure-mathematics","11":"category-combined-mathematics","12":"tag-1023","13":"tag-angle","14":"tag-anukramanaya","15":"tag-combined","16":"tag-coordinates","17":"tag-derivate","18":"tag-direction","19":"tag-geometry","20":"tag-intersect","21":"tag-lakshaya","22":"tag-line","23":"tag-lines","24":"tag-negative","25":"tag-peo","26":"tag-peo-maths","27":"tag-point","28":"tag-points","29":"tag-positive","30":"tag-pure","31":"tag-pure-maths","32":"tag-sarala-rekhawa","33":"tag-sequence","34":"tag-sequence-of-line","35":"tag-slope","36":"tag-straight","37":"tag-straight-line","38":"tag-3802","39":"tag-4249","40":"tag-4244","41":"tag-3588","42":"tag-3874"},"_links":{"self":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/13304"}],"collection":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/users\/75"}],"replies":[{"embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/comments?post=13304"}],"version-history":[{"count":61,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/13304\/revisions"}],"predecessor-version":[{"id":35289,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/13304\/revisions\/35289"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/media\/16874"}],"wp:attachment":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/media?parent=13304"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/categories?post=13304"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/tags?post=13304"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}