इकाई दूरी पर xz समतल के समानांतर एक समतल का समीकरण क्या है?

  1. x + z = 1
  2. y = 1
  3. x = z = 1
  4. x = z = 0

Answer (Detailed Solution Below)

Option 2 : y = 1
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Detailed Solution

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अवधारणा:

कुछ विशेष समतलों के लिए मानक समीकरण:

  • x-y समतल के समानांतर वाले समतल में मानक समीकरण z = d होना चाहिए, जहां d = xy समतल से समतल की दूरी
  • y-z समतल के समानांतर वाले समतल में मानक समीकरण x = d होना चाहिए, जहां d = yz समतल से समतल की दूरी
  • x-z समतल के समानांतर वाले समतल में मानक समीकरण y = d होना चाहिए, जहां d = xz समतल से समतल की दूरी

 

 

गणना:

xz समतल का समीकरण y = 0 है।

हम जानते हैं, xz- समतल के समानांतर एक समतल का समीकरण y = d होता है

यहाँ, d = 1

∴ इकाई दूरी पर xz समतल के समानांतर समतल का समीकरण y = 1 होगा

इसलिए, विकल्प (2) सही है।

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