Question
Download Solution PDFसमतल \(\vec{r}\) \((6\hat{i}-3\hat{j}+2\hat{k})\) = 6 से एक बिंदु (2, 5, -3) की दूरी ज्ञात कीजियें।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया:
बिंदु = (2, 5, -3)
समतल का समीकरण: \(\vec{r}\).\((6̂{i}-3̂{j}+2̂{k})\)= 6
संकल्पना:
समतल के सदिश समीकरण में \(\vec{r} = x̂{i} + ŷ{j} + ẑ{k}\) रखने पर कार्तीय रूप में एक समतल का समीकरण लिखा जा सकता है।
सूत्र:
एक समतल ax + by + cz = d से एक बिंदु (p, q, r) की दूरी निम्न द्वारा दी जाती है,
\(D = |\frac{ap + bq + rc -d}{\sqrt{a^2 + b^2 + c^2 }}|\)
हल:
एक समतल के समीकरण को कार्तीय रूप में लिखना :
\(\vec{r}\).\((6̂{i}-3̂{j}+2̂{k})\) = 6
⇒ (xî + yĵ + zk̂).(6î - 3ĵ + 2k̂) = 6
⇒ 6x -3y + 2z = 6
अब, दूरी सूत्र का प्रयोग करते हुए -
D = \(|\frac{6(2) - 3(5) + 2(-3) -6}{\sqrt{6^2 + (-3)^2 + 2^2 }}|\)
D = 15/7
Last updated on Jun 19, 2025
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