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
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
- [JEE MAIN 2021]
- A
Both $A$ and $R$ are correct and $R$ is the correct explanation of $A$.
- B
$A$ is not correct but $R$ is correct.
- C
Both $A$ and $R$ are correct but $R$ is not the correct explanation of $A$.
- D
$A$ is correct but $R$ is not correct.
Similar Questions
Let $\overrightarrow C = \overrightarrow A + \overrightarrow B$
$(A)$ It is possible to have $| \overrightarrow C | < | \overrightarrow A |$ and $ | \overrightarrow C | < | \overrightarrow B|$
$(B)$ $|\overrightarrow C |$ is always greater than $|\overrightarrow A |$
$(C)$ $|\overrightarrow C |$ may be equal to $|\overrightarrow A | + |\overrightarrow B|$
$(D)$ $|\overrightarrow C |$ is never equal to $|\overrightarrow A | + |\overrightarrow B|$
Which of the above is correct
Let $\overrightarrow C = \overrightarrow A + \overrightarrow B$
$(A)$ It is possible to have $| \overrightarrow C | < | \overrightarrow A |$ and $ | \overrightarrow C | < | \overrightarrow B|$
$(B)$ $|\overrightarrow C |$ is always greater than $|\overrightarrow A |$
$(C)$ $|\overrightarrow C |$ may be equal to $|\overrightarrow A | + |\overrightarrow B|$
$(D)$ $|\overrightarrow C |$ is never equal to $|\overrightarrow A | + |\overrightarrow B|$
Which of the above is correct
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- [JEE MAIN 2024]