IGNOU MTE 3 2026 - उस समतल की समीकरण ज्ञात कीजिए जो समतलों और के प्

Question

उस समतल की समीकरण ज्ञात कीजिए जो समतलों $x + 2y + 3z = 4$ और $4x + 3y + 2z + 1 = 0$ के प्रतिच्छेदन बिंदु से तथा मूल बिंदु से गुजरता है।

09 Jan 2026

Answer :

Word Count : 502

दिए गए समतल हैं: [ \Pi_1: x + 2y + 3z = 4 ] [ \Pi_2: 4x + 3y + 2z + 1 = 0 \implies 4x + 3y + 2z = -1 ] हम वह समतल ढूंढना चाहते हैं जो इन दोनों समतलों के प्रतिच्छेदन रेखा से और मूल बिंदु (O(0,0,0)) से गुजरता हो। चरण 1: प्रतिच्छेदन रेखा का मानक रूप मान लें कि प्रतिच्छेदन रेखा का पैरामीट्रिक रूप है: [ x = \lambda, \quad y = \mu, \quad z = \nu ] इसे (\Pi_1) और (\Pi_2) में डालें: [ \lambda + 2\mu + 3\nu = 4 \quad (1) ] [ 4\lambda + 3\mu + 2\nu = -1 \quad (2) ] (\nu = t) मान लें। (1) से: (\lambda

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