Question
Download Solution PDFतलों
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFअवधारणा:
जैसा कि हम जानते हैं कि, यदि a1x + b1y + c1z + d1 = 0 = 0 और a2x + b2y + c2z + d2 = 0 दो अलग-अलग तलों का प्रतिनिधित्व करता है, तो गुजरने वाले तल का समीकरण इन तलों का प्रतिच्छेदन द्वारा दिया गया है:
(a1x + b1y + c1z + d1) + λ × (a2x + b2y + c2z + d2) = 0.
गणना:
दिया गया:
इन तलों को कार्तीय रूप में बदलिए।
अतः
⇒ x + y + z = 6 ........(1)
इसी प्रकार,
⇒ 2x + 3y + 4z = -5 .........(2)
तो, दो दिए गए तलों के प्रतिच्छेदन से गुजरने वाला तल है:
⇒ (x + y + z – 6) + λ × (2x +3y + 4z + 5) = 0
∵ दिया है कि दिए गए दो तलों के प्रतिच्छेद से गुजरने वाला तल भी बिंदु (1, 1, 1) से होकर जाता है।
⇒ बिंदु (3, 2, 1) समीकरण (1) को संतुष्ट करेगा
⇒ (1 + 1 + 1 - 6) + λ × (2 + 3 + 4 + 5) = 0 ⇒ λ = 3/14.
इसलिए, समीकरण (1) में λ का मान रखने पर, हम प्राप्त हैं
⇒ (x + y + z – 6) + (3/14) × (2x +3y + 4z + 5) = 0
20x +23y + 26z = 69
⇒ (x + y + z – 6) + (3/14) × (2x +3y + 4z + 5) = 0
Last updated on Jul 14, 2025
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