यदि  समतलीय हैं, तो किसके बराबर है?

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NDA (Held On: 18 Apr 2021) Maths Previous Year paper
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  1. 114
  2. 66
  3. 0
  4. -66

Answer (Detailed Solution Below)

Option 3 : 0
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NDA 01/2025: English Subject Test
30 Qs. 120 Marks 30 Mins

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अवधारणा:

अदिश त्रिक गुणनफल के गुण

  • [a b c] = [b c a] = [c a b]
  • [a b c] = - [b a c] = - [c b a] = - [a c b]
  • [(a + b) c d] = [a c d] + [b c d]
  • [λa, b c] = λ [a b c]
  • तीन गैर-शून्य सदिश  समतलीय हैं यदि और केवल यदि [abc] = 0

गणना :

दिया गया: समतलीय हैं यानी

और

जैसा कि हम जानते हैं कि, [a b c] = [b c a] = [c a b]

जैसा कि हम जानते हैं कि, [λa, b c] = λ [a b c]

जैसा कि हम जानते हैं कि, सदिश समतलीय केवल तब होता है यदि [abc] = 0

⇒ 

अत: सही विकल्प 3 है।

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