Question
Download Solution PDFमूल से तल 4x - 2y + 3z - 6 = 0 तक खींचे गए लंब के पाद के सह-निर्देशांक ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
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तल : 4x - 2y + 3z - 6 = 0
अवधारणा:
समीकरण ax + by + cz = d(a, b, c) वाले तल के लिए तल के अभिलंब के दिशा अनुपात हैं।
(x1, y1, z1) से गुजरने वाली रेखा का समीकरण और कार्तीय रूप में दिशा अनुपात a, b, c है:
\(\frac{x-x_{1}}{a}=\frac{y-y_{1}}{b}= \frac{z-z_{1}}{c}\)
गणना:
समतल के लम्बवत् दिशा अनुपात 4 , -2 , और 3 हैं।
मूल (0, 0, 0) और 4, -2, 3 दिशा अनुपात से गुजरने वाली रेखा का समीकरण है:
\(\frac{x-0}{4}=\frac{y-0}{-2}= \frac{z-0}{3} = λ\)
⇒ x = 4λ , y = -2 λ और z = 3λ
उपरोक्त निर्देशांकों के साथ तल का सन्तोषजनक समीकरण :
⇒ 4(4λ) - 2(-2λ) + 3(3λ) - 6 = 0
⇒ λ = 6/29
∴ लंब का पाद,
⇒ x = 24/29, y = -12/29 और z = 18/29
Last updated on May 26, 2025
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