Question
Download Solution PDFएक समीकरण का समतल (1, -1, 2) से होकर गुजरता है और इसका द्विक अनुपात (1, 2, 3) है समीकरण का मान ज्ञात कीजिये।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFव्याख्या:
एक समतल सदिश बिंदु \(\overrightarrow{a}=i-j+2k\) से होकर गुजरता है और इसमें सामान्य सदिश का मान \(\overrightarrow{n}=i+2j+3k\) है।
इसलिए, समतल का सदिश समीकरण होगा-
\((\overrightarrow{r}-\overrightarrow{a}).\overrightarrow{n}=0\)
⇒ \(\overrightarrow{r}.\overrightarrow{n}=\overrightarrow{a}.\overrightarrow{n}\)
⇒ \(\overrightarrow{r}.(i+2j+3k)=(i-j+2k).(i+2j+3k)\)
माना \(\overrightarrow{r}=xi+yj+zk\)
⇒ \((xi+yj+zk).(i+2j+3k)=(i-j+2k).(i+2j+3k)\)
⇒ x + 2y + 3z = 1 - 2 + 6
⇒ x + 2y + 3z = 5
इसलिए, समतल का कार्तीय समीकरण x + 2y + 3z = 5 है।
Last updated on Jun 19, 2025
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