Question
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निर्देश: निम्नलिखित प्रश्नों के लिए निम्नलिखित को ध्यान में रखें:
माना L : x + y + z + 4 = 0 = 2x - y - z + 8 एक रेखा है और P : x + 2y + 3z + 1 = 0 एक समतल है।
रेखा के दिक् अनुपात क्या हैं?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFव्याख्या:
दिया गया है:
L = x + y + z + 4 = 0 = 2x - y - z + 8 और
P = x + 2y + 3z + 1 = 0 एक समतल है।
⇒ माना रेखा के दिक् अनुपात (a, b, c) हैं
चूँकि रेखा समतलों के प्रतिच्छेदन से प्राप्त होती है।
⇒ x + y + z + 4 = 0 और 2x - y - z + 8 = 0
इसलिए a + b + c = 0....(i)
⇒ 2a - b - c = 0...(ii)
(i) और (ii) को हल कीजिए
⇒\(\frac{a}{-1+1} = \frac{b}{2+1} = \frac{c}{-1-2} =λ \)
⇒ a = 0, b = 3λ और c = -3λ
⇒ रेखा के दिक् अनुपात (0, 3, -3) या (0, 1, -1) हैं।
∴ विकल्प (c) सही है।
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