Question
Download Solution PDFतल 3x - 6y + 2z + 11 = 0 से बिंदु (2, 3, 4) की दूरी ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
एक तल से एक बिंदु की लम्बवत दूरी:
आइये कार्तीय समीकरण, Ax + By + Cz = d द्वारा दिए गए एक तल, और एक बिंदु जिसका निर्देशांक (x1, y1, z1) हैं पर विचार करते हैं। इसलिए,
\(Distance = \left | \frac{Ax_{1} + By_{1} + Cz_{1} - d}{\sqrt{A^{2}+ B^{2}+C^{2}}} \right |\)
गणना:
हमें तल 3x - 6y + 2z + 11 = 0 से बिंदु (2, 3, 4) की दूरी ज्ञात करनी है
\(⇒ Distance = \left | \frac{3\times 2 \ + \ (-6)\times 3 \ + \ 2\times 4 \ + \ 11}{\sqrt{3^{2}+ (-6)^{2}+2^{2}}} \right |\)
\(⇒ Distance = \left | \frac{6 \ - \ 18 \ + \ 8 \ + \ 11}{\sqrt{9 \ + \ 36 \ + \ 4}} \right |\)
\(⇒ Distance = \left | \frac{7}{\sqrt{49}} \right |\)
⇒ दूरी = 1
अत:, तल 3x - 6y + 2z + 11 = 0 से बिंदु (2, 3, 4) की दूरी 1 इकाई है।
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