Question
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निर्देश: निम्नलिखित प्रश्नों के लिए निम्नलिखित को ध्यान में रखें:
माना S दो समतलों x + y + z = 1 और 2x + 3y - 4z = 8 का प्रतिच्छेदन रेखा है।
निम्नलिखित में से कौन S के दिक् अनुपात हैं?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFव्याख्या:
दिया गया है:
⇒ दो समतल x + y + z = 1 और 2x + 3y - 4z = 8 हैं।
मान लीजिये कि a, b, c समतलों के प्रतिच्छेदन रेखा के दिक् अनुपात हैं।
तब रेखा दोनों समतलों के अभिलम्ब पर लम्बवत है
⇒ a + b + c = 0 ...(i)
⇒ 2a + 3b - 4c = 0 ....(ii)
⇒ \(\frac{a}{-4-3} = \frac{b}{2+4} = \frac{c}{3-2} = λ \)
⇒ a = - 7λ, b = 6λ, c = λ
इस प्रकार, दिक् अनुपात (-7, 6, 1) हैं।
∴ विकल्प (b) सही है
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