ABC

एक त्रिभुज है, जो B पर समकोणीय है। यदि त्रिभुज के शीर्ष A(k,1,1), B(2k,0,2) और C(2+2k,k,1) हैं, तो k का मान क्या है?

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NDA-I (Mathematics) Official Paper (Held On: 13 Apr, 2025)
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  1. -3
  2. -1
  3. 1
  4. 3

Answer (Detailed Solution Below)

Option 4 : 3
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गणना:

दिया गया है,

बिंदु A(k, 1, -1), B(2k, 0, 2), और C(2 + 2k, k, 1) त्रिभुज के शीर्ष हैं।

सदिश AB और BC इस प्रकार दिए गए हैं:

और का अदिश गुणनफल है:

चूँकि सदिश लंबवत हैं, इसलिए उनका अदिश गुणनफल शून्य होना चाहिए:

इस प्रकार, .

∴ k का मान है।

इसलिए, सही उत्तर विकल्प 4 है।

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