JEE Mains · Physics · STD 11 - Vectors
- JEE Mains 2021
- Hard
- MCQ
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
Pick an option to check your answer.
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,
\(\overrightarrow{ AB }=\overrightarrow{ AO }+\overrightarrow{ OB }\)
\(\overrightarrow{ AC }=\overrightarrow{ AO }+\overrightarrow{ OC }\)
\(\overrightarrow{ AD }=\overrightarrow{ AO }+\overrightarrow{ OD }=2 \overrightarrow{ AO }\)
After adding all, we get,
\(\overrightarrow{A B}+\overrightarrow{A C}+\overrightarrow{A D}=4 \overrightarrow{A O}+\overrightarrow{O B}+\overrightarrow{O C}\)
Reason \(R\) is the direct result of Polygon law of vector addition
Therefore, Polygon law is applicable in both but the equation given in the reason is not useful in explaining the assertion.
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