समानांतर तल 3x + y + 3z = 8 और 9x + 3y + 9z = 15 के बीच की दूरी क्या है?

  1. \(\frac{5}{{\sqrt 19}}\)
  2. \(\frac{7}{{\sqrt 19}}\)
  3. \(\frac{3}{{\sqrt 19}}\)
  4. \(\frac{9}{{\sqrt 19}}\)

Answer (Detailed Solution Below)

Option 3 : \(\frac{3}{{\sqrt 19}}\)
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संकल्पना:

दो समानांतर तल ax + by + cz + d1 = 0 और ax + by + cz + d2 = 0 के बीच की दूरी \(\rm |\frac{d_1-d_2}{\sqrt{a^2+b^2+c^2}}|\) है। 

 

गणना:

यहाँ, 3x + y + 3z = 8 और 9x + 3y + 9z = 15 

 9x + 3y + 9z = 15 को 3 से विभाजित करने पर हमें निम्न प्राप्त होता है

अब, 3x + y + 3z = 8 और 3x + y + 3z = 5 के बीच की दूरी 

\(\rm= |\frac{8-5}{\sqrt{3^2+1^2+3^2}}|\\ =\frac{3}{\sqrt{19}}\)

अतः विकल्प (3) सही है। 

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