शीर्ष (0,2,2), (2,0,-1) और (3,4,0) वाले त्रिभुज का क्षेत्रफल क्या है?

  1. 15/2 वर्ग इकाई 
  2. 7/3 वर्ग इकाई 
  3. 15 वर्ग इकाई 
  4. 1/5 वर्ग इकाई 

Answer (Detailed Solution Below)

Option 1 : 15/2 वर्ग इकाई 
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Detailed Solution

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संकल्पना:

जब दो सदिश दिए गए हैं, तो त्रिभुज का क्षेत्रफल:

पार गुणनफल:

 

गणना:

यहाँ, माना कि A = (0,2,2), B = (2,0,-1) और C =(3,4,0) है। 

AB = (2-0, 0-2, -1-2) = (2, -2, -3) और 

AC = (3-0, 4-2, 0-2) = (3, 2, -2)

त्रिभुज का क्षेत्रफल = 

 

=1/2(10 i + 5 j + 10 k)

= 1/2 √(100 + 25 + 100)

= 15/2 वर्ग इकाई 

अतः विकल्प (1) सही है। 

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