बिंदु A और B के स्थान सदिश क्रमशः 3î - 5ĵ + 2k̂ और î + ĵ - k̂ हैं। तो AB की लम्बाई क्या है?

  1. 11
  2. 9
  3. 7
  4. 6

Answer (Detailed Solution Below)

Option 3 : 7
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Detailed Solution

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संकल्पना:

माना कि \(\rm {\rm{\vec a}} = {\rm{x\;\vec i}} + {\rm{y\;\vec j}} + {\rm{z\;\vec k}}\) है, तो \(\vec a\) के सदिश का परिमाण =\(\left| {{\rm{\vec a}}} \right| = {\rm{\;}}\sqrt {{{\rm{x}}^2} + {\rm{\;}}{{\rm{y}}^2} + {{\rm{z}}^2}} \)

गणना:

दिया गया है:

बिंदु A और B के स्थान सदिश क्रमशः 3î - 5ĵ + 2k̂ और î + ĵ - k̂ हैं। 

\(\rm \vec{AB} = \rm \vec{B}-\rm \vec{A}\)

⇒ \(\rm \vec{AB} =\)  (î + ĵ - k̂) - (3î - 5ĵ + 2k̂)

\(\rm \vec{AB}= -2\rm\hat{i} + 6\rm\hat{j} -3\rm\hat{k} \)

अब, \(\vec {AB} \) की लम्बाई  \(= \rm |\vec {AB}|\)

⇒ \(\rm |\vec {AB}|\) \(\sqrt{(-2)^2+6^2+(-3)^2} = \sqrt{49}=7\)

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