उस समतल के सदिश और कार्तीय समीकरण ज्ञात कीजिए जो बिंदु (5, 2, -4) से होकर गुजरता हैं और दिशा अनुपात 2, 3, -1 के साथ रेखा के लंबवत हैं?

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  1. x + 2y - 3z = 18
  2. 2x + 3y - z = 20
  3. 2x + 3y - 5y = 24
  4. 2x + 5y - 7z = 15

Answer (Detailed Solution Below)

Option 2 : 2x + 3y - z = 20
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दिया गया है:

वह समतल जो बिंदु (5, 2, -4) से होकर गुजरता है।

समतल दिशा अनुपात 2, 3, -1 के साथ रेखा के लंबवत है।

संकल्पना:

(x1 , y1 , z1के माध्यम से गुजरने वाले समतल का कार्तीय समीकरण और drs a, b, c वाली रेखा के लम्बवत समीकरण निम्न द्वारा दिया जाता है:

a(x - x1) + b(y - y1) + c(z - z1) = 0

हल:

समतल का समीकरण:

2(x - 5) + 3(y - 2) -(z - (-4)) = 0

⇒ 2x + 3y - z = 20

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