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JEE Mains · Physics · STD 11 - 3.1 vectors

Assertion \(A\) : If \(A, B, C, D\) are four points on a semi-circular arc with centre at \('O'\) such that \(|\overrightarrow{{AB}}|=|\overrightarrow{{BC}}|=|\overrightarrow{{CD}}|\), then \(\overrightarrow{{AB}}+\overrightarrow{{AC}}+\overrightarrow{{AD}}=4 \overrightarrow{{AO}}+\overrightarrow{{OB}}+\overrightarrow{{OC}}\) Reason \(R\) : Polygon law of vector addition yields \(\overrightarrow{A B}+\overrightarrow{B C}+\overrightarrow{C D}+\overrightarrow{A D}=2 \overrightarrow{A O}\) In the light of the above statements, choose the most appropriate answer from the options given below

  1. A Both \(A\) and \(R\) are correct and \(R\) is the correct explanation of \(A\).
  2. B \(A\) is not correct but \(R\) is correct.
  3. C Both \(A\) and \(R\) are correct but \(R\) is not the correct explanation of \(A\).
  4. D \(A\) is correct but \(R\) is not correct.
Verified Solution

Answer & Solution

Correct Answer

(C) Both \(A\) and \(R\) are correct but \(R\) is not the correct explanation of \(A\).

Step-by-step Solution

Detailed explanation

\(|\overrightarrow{A B}|=|\overrightarrow{B C}|=|\overrightarrow{C D}|\) Here, \(O\) is the centre of semi- circle \(\therefore|\overrightarrow{O A}|=|\overrightarrow{O B}|=|\overrightarrow{O C}|=|\overrightarrow{O D}|\) Using vector law of addition, we can write,…
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